I have been a consultant at a Big 4 (not Deloitte) firm in London (our targets are top universities Oxford, Cambridge, Warwick, LSE, UCL, Edinburgh) for just under a year and have an offer from Deloitte in Strategy but it would involve starting again as a business analyst, basically starting from scratch. Is the variety of work, B-schools opportunities and the prestige worth the restart? Any other thoughts?

No. The Big4 are not distinguished in terms of b-school entry or prestige and you will be sorely disappointed by how little difference there is in the work between Deloitte's "strategy" group and what you do now especially as an Analyst.

Yes. Deloitte S&O is as picky in selection as the other strategy consultants and are actively trying to expand their strategy practice. The work you do is the same of the Strategy houses. In comparision: I've just been to recruitment events of McKinsey and OC&C and "pure strategy" is estimated to be 25% of their work areas. There is plenty of operational work everywhere. As an added bonus, they pay more than MBB:http://www.consultingmag.com/article/ART647748which is like 60% more than a first year analyst in their normal divisions would get.

Just noticed you posted the exact same thing on wallstreetoasis.com and got a similair reply ^^

They've been "actively trying to expand their strategy practice" for a long time. Doesn't mean it will happen.Meet the people and ask them what the work is.