One thing that seemed to make customers relaxed about the banks in Turkey was to inform them that a number of them were in the safe ownership of large, respected European banks (Finans, ING/Oyak etc.) - maybe now those that aren't may be a safer bet? As discussed somewhere else, Turkish banks tend to be wealthy with cash assets rather than property and the like. Cash tends to get an easier ride in turbulent times, certainly when compared to capital assets - which can be heavily hit in a recession - and for that reason, it is likely that Turkish banks will not be as exposed as UK and European ones.
The only other consideration might be the exchange rate, if you want to return your Lira to Sterling. As long as Turkey keeps it's economy equally as healthy or unhealthy as the UK, not much will change there