A few more airlines from the 1980s...

Aerotour from France - a couple of 737-200 for a just a few months in 1980
Air Sul from Portugal - started operations at the very end of 1989 with a 737 leased from Britannia AW
Eagle Air of Iceland - several aircraft flown at various points from 1982 onwards, including leasing to Britannia AW
Rotterdam Airlines from Holland - another short lived airline, but unsure whether they were mostly scheduled or charter
Transwede from Sweden - used 737s from 1989

If we're including Turkey, then there are the following
Istanbul Airlines (a single 737-400 ! - does this count?)
Sultan Air

There may be more out there...

Paramount ended up with both of the AmberAir 737-200s and their own 737-300 (G-PATE) which was based at Newcastle. They had four MD83s as well in that final year in which their bank account was emptied and ILG had to prop them up to complete the summer flying programme rather than see the airline collapse mid-way through the summer.

GB Airways leased a 737 from Britannia for a weekly Gibraltar flight for many years through the mid 1980s before they obtained their own 737-200s and the relationship with BA really moved on. It made substantial money for a few years but the timing of the sale by Bland Group to easyJet was probably one of the better outcomes in aviation history for airline owners. They got out at a good time just before the market chaos, fuel prices and mass bankruptcies that followed in 2008. It was certainly one of the more astute pieces of Gatwick history, especially when compared to the likes of BIA turning down a take-over offer from Air Europe largely based on the value of Gatwick slots, only for BIA to fail within 18 months.

To answer your question....No Peach Air was not a reincarnation of Sabre.

Peach Air started operations in 1997 and was taken over by JMC Airlines in 1999.

Peach Air operated four aircraft, two Boeing 737-200 and two Lockheed L1011, none of which saw further flying with JMC Airlines.

Sabre started operations in 1994 and was taken over by Excel Airways in 2001.

Sabre Airlines two original Boeing 737-200 aircraft which were both leased went onto Peach Air in 1997. The two Boeing 737-200 in question were, G-SBEA delivered in April 1997 and G-SBEB delivered in January 1997.

Sabre operated Boeing 727-200, Boeing 737-200, Boeing 737-800, but not simultaneously.
Sabre was the first UK airline to operate the Boeing 737-800 with the initial aircraft being delivered to the airline in January 2000.

Olympic Airways certainly operated their Boeing 737-200's beyond the south east Mediterranean.

In the early to mid eighties when Olympic Airways withdrew their fleet of Boeing 720's the airline operated their Boeing 737-200 aircraft on the summer only schedule from London Heathrow to Thessaloniki. At the same time Olympic Airways also flew a summer seasonal scheduled flight from London Heathrow to Corfu which was operated by their Airbus A300's.

Olympic Airways Boeing 737's we're often seen at northern European airports such as Amsterdam, Frankfurt, Geneva, London Heathrow, Paris CDG.

https://cimg3.ibsrv.net/gimg/pprune....828d18857e.jpg
Olympic Airways Boeing 737-284 SX-BCI at London Heathrow Airport in July 1986.

Back then it was a different place, the instability that has plagued Liberia since the early 80's wasn't in full swing and the class with money and power still had it relatively good. I met a black English DJ in a hotel disco in Bangkok in 85, who had just come from a 6-month stint in the top nightclub in Monrovia and he said it was amazing, a crazy place for party people. Perhaps the Air Liberia flights were bringing adventurous travellers out during the season. All the same, that's a long flight in a 737.

Dassault Mercures would have been operating to/from the French Mediterranean

They did do some flights into LHR subbing for Air France here and there, but Air Inter's Mercure aircraft did the Paris Orly-Nice and Marseille routes until the A300's took over. These were just internal trunk routes rather than holiday flights. I flew in one a bit later between Paris Orly and Avignon just before they were retired and sent out to various museums.

Abelag and Air Belgium - or were they one and the same?!

They also operated, around 1989, an Air France-badged/coded route from Paris to Gatwick. Given that they had the JT8D off the 737-200 and slightly looked like an oversized one as well, they possibly qualify for a peripheral mention here.

Might be their only international schedule for the grand fleet of 10 outside France. When Airbus first wanted to do the A320 there were several doubters who pointed to the Mercure and said it was the same size and would have the same sales fate.

You know the rest ...

You might well be correct, but I have the inkling that they 'might' have been used on the Paris-Brussels and Paris-Geneva routes at one time. The Geneva route would've been technically an internal flight as it would have landed and taxied to the French side of the terminal. I liked the Mercure and subsequent visits to museums where they are resident, including internal tours, showed they were ahead of their time. Almost like the French Trident/VC-10 in respect of it's international appeal.

Palm Air still used a 737-200 based at Hurn up to November 2008. Operated mainly to the Med, They later used a Astraeus -500 up to the point that they stopped trading in Oct 2010.

Aerosvit were still operating a B737-200, which would have served some Mediterranean destinations, until their bankruptcy in 2013.

What a thread and what a drift, got me thinking of KLM DC4 but, Mooncrest, Air Florida XL also did a stint with Air Europe in, around 1984. Without log-book check, I think I would have flown it a few times and a mate of mine did the ferry trip over from Miami, via Goose to LGW at the start of the summer season. Didn't it crash with the icing problem in some river back in the USA after seeing time on the UK IT network summers ?

N62AF was the Potomac River crash Air Florida 737 - an ex United -222, I don't think it ever operated in Europe.

IIRC, the Air Florida 732s that Air Europe and Dan Air borrowed were both the -2T4 variant.

737-200 holiday jets 70's/80's
 

737-200 charter jets

Air UK Leisure started with some -200's
I think GB Airways Leisure was mentioned
MEY AIR
TEA
TEA UK
Air Berlin USA
Luxair

Later years I think - all French... still using -200's
Euralair
aigle azur
corsair
ACI
EAS
Air Toulouse

COPA flight 201, a Boeing 737-204Adv, which crashed on 6th June 1992, was ex-Britannia G-BGYL, which would have carried many thousands of us on bucket and spade and snow plough runs before its untimely dive into the Panamanian jungle. I flew on her 10.02.83 LTN - GVA on my last school ski-trip (back on BFVB)

Like a number of the "captive" holiday flight divisions of mainstream carriers, they did substitute operations for their parent, especially in the off season.

I recall being at Stansted for an AirUK 146 to Edinburgh. This particular day it was being operated by one of their 737s. They must have had a separate AOC, and CAA rules require that pax are specifically told which AOC they are on. So there was a stack of leaflets to this effect being handed out at check-in, written in rather poor aviationese. In front of me were an elderly couple, also for Edinburgh. "Yeah, to Edinburgh, yeah. It's a Leisure flight today, yeah ...". Which of course was all complete double-dutch to them.

Yes I guess so as Air UK leisure was a joint venture with the parent Co. Air UK, and with Viking (a seat broker)
In addition the 767-300ER purchase was a Unijet collaboration and these 767's never carried Air UK Leisure titles - They were just Leisure, when in 1993 the airline introduced two leased Boeing 767-300ER aircraft on behalf of tour operator Unijet.

Leisure International Airways
In 1996 the airline was completely sold to Unijet and was renamed Leisure International Airways and moved its main base to LGW.

There was a full winter season where the scheduled AirUK early morning LGW-EDI-GLA-LGW circular flight was operated by an Air UK Leisure 737 (which I think was a -400 by then) before it set off to the Canaries or wherever at about 1100.

Going back to an earlier topic, I've checked the schedule books for NCL for 1985 and 1988 and can find no record of BA operating IT charters overnight from there - which was what I thought. They were doing this from MAN, GLA, BFS and to a lesser extent EDI but there were no regular BA charters shown ex NCL. In 1985, the NCL-LHR service was a 737-200 on the Newcastle nightstop and a mix of 737-200s and 1-11-500s plus a Trident 3 each afternoon. By 1988 it was a 757 on the nightstop and evening up & back (where the Trident 3 used to be) and still 737-200s and 1-11-500s on the rest. Newcastle was one of the few (only?0 BA domestic destinations to regularly see the A320s and also the four 737-300s which BA leased from Maersk for a couple of years around 1990-1992.