Why are you trying to get a private one, is it because you are curious but have no symptoms? Just asking. I have had several at BUPA but as part of a package, you could try calling them and see if they could quote you for just a stress test, or try Spire Hospitals and do the same. Some sports venues may be worth a shot, I live in Glasgow and happen to know you can get one at Hampden for £120
and they have a cardiology professor on the team to do the interpretation.
Usually if you do a VO2max test they will hook you up to an ecg too but you may not have someone fully qualified to interpret it so not a good route in this case. I got a VO2max test with ecg at UEA for £50 once but not sure they do it anymore.
I'm on Warfarin for life now and my cardiologist and rehab team had no issues with me running whilst on it. Can't see any reason why they should, either.
However I did have one nasty fall when my shin got caught by a loose manhole cover and got cut very badly and it wasn't fun without any clotting so had to go straight to A&E to get it looked at. Other than that, no probs at all.