Fuel economy is an interesting thing, my Cub with it's C90 engine drinks a little under 18ltrs mogas an hour. I have a friend with an RV4 which is probably about 28 litres AVGAS an hour but I get 75 kts and he gets 160kts. So per hour I'm cheaper but distance wise he's significantly less expensive.
VLAs as far as I'm aware none of them are cleared for IFR flight and I have to say I wouldn't want to either
they bounce around a bit in fairly smooth conditions.
That said, the LAA is well under way for getting appropriately equipped aircraft certified to fly IMC/IFR. So you should not be turned off too much by LAA aircraft so long as they have the gear, not sure how long it will take but it will happen.
Suggestions for consideration, with a budget of £130k you have a lot of options.
1. It should be easily resold, nothing worse than having a rare non desirable aircraft, so be warned - if you decide to sell it on and chose something rare you will find difficulty selling it on.
2. Spares, it should be easy and not too expensive to find spares. For instance the TB20 you can find spares for but they're rarely cheap, the TB10 is a different matter entirely. Cessnas and Pipers are much easier but anything with a CofA requires a form 1 along with it, it translates to a great deal more expense for a piece of paper.
3. It should not prevent you from landing at almost any airfield you want, so if you need something that does grass, get something that's good on grass. It might mean high wing.
With your budget in mind, if it was me buying the aircraft.
Vans RV8/RV7, the tailwheel version. Imports can be total garbage but the UK home built ones tend to be very good, even if they aren't they'll provide good economy for range and are likely to be well equipped for IFR flight, if not you can use the £50k you'll have left over to equip for IF.
All of the RVs are fast up to about 200mph, many of them can/do run on MOGAS. I don't like the nosewheel ones but without any real justification.
Carbon Cub SS. Probably not as fast as you're looking for but well equipped, on an EASA Permit ready to fly, it's new and a seriously good bit of kit. I want one to the core of my bones
. There is no airfield in the UK that would be difficult to get into.
Super Decathlon, or one of the other ACA aircraft. Fast enough, economy isn't quite what you want but will be certified for IFR and you can buy new with your budget. Very comfortable tourer lots of space, lots of useful load and should provide you with the range you desire. I've flown a couple of these and like them a lot.
Cessna 182 Q (or later) or RG, you probably wont like the thirst of this machine but it will get you in anywhere and is plenty quick enough, there are N reg ones around that come with long range tanks, have plenty of bells and whistles, are certified for IFR are popular enough to resell and parts are easily attained.
TB20, plenty around to buy, very fast, parts can be pricey and a pain to get but for touring, my belief is that there is nothing more comfortable. You wont get mogas in it
Also fairly thirsty but again, speed provides the economy.
The Sportcruiser is nice, the noseleg is weak and my understanding is from a reliable source that after a couple of replacement noselegs, other stuff starts to warp and bend. Care is required on landing.
Still a Vans will do all you expect and significantly more, an RV 7 with a 180hp engine would do what you want and you'll have plently left over to cover the costs of more fuel used per hour - also the maintenance will be significantly cheaper. That's what I'd have