On some bikes, with some tyre combinations, I've run mismatched tyres perfectly fine - and on others I've experienced serious juddering and a tendency to tank-slap.
If it works out cheaper or significantly more convenient to change them both at the same time, I'd do that.
If you can't save much by doing everything together, and it isn't really a hassle to get to the tyre place twice, what I'd do is budget for both, but replace the rear first. Then, if there were problems with vibration, handling or anything, you could take it straight back and have the front replaced - and if there are no problems you've saved yourself £150-odd!