Mat777.
There is a Soviet Yak single engined advanced trainer based at Sleap which may fit the description of your interesting aeroplane. It certainly zooms about a lot around the North Shropshire and South Cheshire area.
Pilots operating in the Manchester Low Level Route are not obliged to call Manchester Approach, but just to listen out and use a discreet squawk which enables the Manchester controller to positively identify the aeroplane if it starts to wander outside the corridor and near to Manchester airport.
I fly through the corridor quite often and just listen out so if you were hoping to correlate your sightings with specific radio callsigns on the radio you may be disappointed.