Not from my experience, WWE is still way ahead of TNA in the popularity stakes, the only real advantage that TNA would have in the UK is that it currently airs and will continue to air on Challenge TV, which to translate how that sits compared to the US, Challenge TV is on what's called Freeview, which is broadcast television that doesn't need any subscription, cable or satellite to watch.
WWE however is broadcast on Sky Sports which is primarily a satellite channel but you can also get it on cable, but the packages to get Sky Sports on are fairly pricey so that does put people off, plus the scheduling is shocking. Raw airs live so starts at around 1 or 2 in the morning (depending on Daylight savings etc), the replay is on Thursday at 6:00pm and is cut with the old 'freeze-frame chair shots'... urm-yeah. Smackdown airs on Friday, NXT is sometime, as is Superstars, but because there is 4 Sky Sports channels they chop and change which of the 4 they are going to show it on, then changes the time of day and the day it's shown, even for Raw so you can never keep up properly. The other added annoyance, is because Sky like to package either Sky Sports 1-3 together or 1 & 3 or 2 & 4 or 1-4, you basically have to purchase the whole package to see the complete WWE output, but then you're stuck with a load of sports you don't even watch.
I would hope for one of two things, the WWE Network is streaming and becomes successful so they can export the idea to other countries like the UK, or Sky lose the rights to someone who gives a sh*t.