They won't imo.
It's a very interesting question. To be honest I think that many European countries have already got governments which, in their ideology if not their actions, would be considered to be on the far right on a political and economic scale, and many countries which are adopting racist policies in plain sight of the rest of the EU. The far right doesn't automatically equal fascism. Remember that the majority of Europe's governments before fascism appeared as a mass movement, and even in some cases, afterwards, were extremely conservative, even racist by today's standards. Homosexuality was only legalised in 1967 here, but the government we had before that was not fascist. What we are seeing IMO is the gradual abandonment of liberal democracy (but not "democracy" itself with elections etc) to coincide with declining wages, increased industrial/civil unrest etc. Actually it's always been there - given the police response during the miners' strike etc. It's just that as the booms/recoveries get shorter every time and less frequent and the recessions get longer and more severe, more state sanctioned violence, racism, etc, will increasingly become the norm. That's not the same as fascism however.
The "revolutionary" right (ie fash) poses as much of a threat to the existing order as does the revolutionary left. Fascism was a disaster for capitalism during and after the 2nd world war in terms of the destruction it caused, the wealth lost, the people/resources lost or deliberately shut out of the "market" etc. I don't think that the present British government (I'm assuming that you're talking as if the current government are still in power)? would want to encourage a fascist government in Europe which appeared to present a valid alternative to neo-liberal capitalism, especially given the fragility of the coalition. They'd probably waver between ignoring it/adopting some of the policies and condemning it from time to time.
Ultimately though I don't think that, at least in western europe, a fascist party is going to come to power. The danger from the far-right comes from the level to which these ideas have now been normalised and adopted by mainstream governments. And you certainly won't find the British government saying anything against Sarkozy and co