Heres all 80s cars, any aspiration, under 6k
http://www.pistonheads.com/classifieds/used-cars/tvr/wedges/1986-350i-convertible-stunning/2414927?isexperiment=true
TVR 350i - don't know about parts availability and mod potential for these cars. TVRs always interested me.this is a Rover V8 TVR so huge potential on the power front. 4995
http://www.pistonheads.com/classifieds/used-cars/porsche/944/porsche-944-s-1988/2681252?isexperiment=true
944S old man owned 3450 160k miles
http://www.pistonheads.com/classifieds/used-cars/tvr/classics/1987-tvr-tasmin-2-8i/2495156?isexperiment=true
TVR Tasmin 2995
http://www.pistonheads.com/classifieds/used-cars/tvr/wedges/tvr-350i-wedge-stunning-crimson-red/1814059?isexperiment=true
TVR 350i that looks great. 5995
http://www.pistonheads.com/classifieds/used-cars/porsche/944/porsche-944s2/2595685?isexperiment=true
944S2 4295, i highly recommend these.
http://www.pistonheads.com/classifieds/used-cars/reliant/scimitar/a-sorted-scimitar-gte--over-4k-spent-in-last-4-months-ready-to-enjoy/2495193?isexperiment=true
Scimitar GTE, cool shooting brake car similar to the Capri you like.
http://www.pistonheads.com/classifieds/used-cars/tvr/t350/tvr-350i-3-5-2dr-convertible-low-mileage-1985/2630935?isexperiment=true
another TVR 350 similar to those above
http://www.pistonheads.com/classifieds/used-cars/porsche/924/porsche-924-s-1988/2652546?isexperiment=true
Cheap 944s at 2k
http://www.pistonheads.com/classifieds/used-cars/porsche/944/porsche-944-s--1988/2652341?isexperiment=true
nice 944s at 3.5k
http://www.pistonheads.com/classifieds/used-cars/toyota/mr2/toyota-mr2-t-bar-sports/2649767?isexperiment=true
AW11 MR2 at 5k
http://www.pistonheads.com/classifieds/used-cars/bmw/e30-3-series-82-94/bmw-3-series-325i-sport-e30/2260373?isexperiment=true
325i at 3795, pics look good
http://www.pistonheads.com/classifieds/used-cars/tvr/wedges/for-sale-tvr-350i-s2/2641538?isexperiment=true
again, rover v8 TVR
http://www.pistonheads.com/classifieds/used-cars/ford/capri/ford-capri-2-8i-black-1983/2639689?isexperiment=true
5k capri
http://www.pistonheads.com/classifieds/used-cars/porsche/944/porsche-944-2-5-aug-1982/2496271?isexperiment=true
944 non-s at 4k
http://www.pistonheads.com/classifieds/used-cars/tvr/wedges/tvr-tasmin-1984/2487712?isexperiment=true
another v6 tvr
If you want something ridiculous fast I would skip these and get a skyline above. Don't know anything about the 350i TVRs but if they check out that might be a good option actually. If you like the Capri that Scimitar is cool.
Of all of these I would check out that 944S2 first. That would be a tremendous buy if it's good. If they are around 4k in the UK and you don't want a turbo car that would be one of your best options.
These are all good enthusiast cars though where i'm from TVRs do not have a good reputation.
All the 80s stuff that I really like are more money. If it were me I would get a Skyline that I posted previously though the 944S2 would be tempting.