I think there are in relation to the minimum wage for au pairs
No, not specifically. However there is an exemption from the requirements for the National Minimum Wage for workers in certain conditions where "the worker resides in the family home of the employer for whom he works, [and] the worker is not a member of that family, but is treated as such, in particular as regards to the provision of accommodation and meals and the sharing of tasks and leisure activities". Most au pairs and many live-in nannies fit this description, although interpretation of "sharing of leisure activities" is somewhat troublesome.
but sole charge is not an au pair anyway so that is not relevant.
There is no legal definition of an au pair in the UK. The only regulations where the term is used is in relation to the Accession Worker Scheme for Bulgarian and Romanian nationals where "au pair" is one of the limited number of occupations that such a national can work in. However there is no definition of what constitutes an "au pair" and as "domestic employee in a private household" is another such occupation with exactly the same treatment, and "au pairs" are clearly a subset of this category, there is little relevance to any restriction.
I wonder how they work out how much the benefit of free board and lodging is worth in working out if someone is paid more than the minimum wage?
This is called the National Minimum Wage Accomodation Offset and it is set arbitrarily at £4.82 a day or £33.74 a week. No other offset is permitted, including any for food or any other aspect of board, however for workers that fall within the exemption mentioned above this is irrelevant.