Be careful about mentioning a particular person. Or if you do, try to ask or find out somehow whether or not A) they will be on sabbatical or research leave in your first year B) will be retiring in the next two years or C) are in the middle of the ESRC project. From experience I know that A and B could immediately kill your chances of working for them, and if it's the only relevant person in the Department it'd be a high-risk application and there would be supervisory issues that could place an acceptance in jeopardy. For C, there are a few scholars that won't take new supervisees the years they are on an ESRC-project. Some universities may even have separate more specialized apps for this (not sure about Oxford in particular).