What is the best legal set-up in the UK?

It's hard to say, because much will depend on how the fund is meant to operate. You would need to take advice based on your specific circumstances. Both options are easy to set up and operate so that isn't a factor. A limited company may be a little less flexible on profit sharing but that isn't impossible to overcome. More important is to what extent you need to retain profits: in a roll-up you probably intend to retain profits and use them to buy more businesses; if so a ltd company is almost certainly going to be better, because you can retain profits with only a deduction for corporation tax (~19-25%) instead of having to (in an LLP) pay yourself, deduct ~40% for taxes, and reinvest the remainder in your next acquisition. I've assumed here that your businesses will derive their profits from trading in the UK. Another example: debt is usually easier for LTDs to raise than for LLPs, though again YMMV because it depends who the partners actually are and where they're based. So there is no best—it depends on many things: source of profits (UK vs ex-UK), plans for retaining/reinvesting profits, circumstances of the partners in the business, whether you plan to borrow in the UK or not, and what commercial arrangement you want to offer to the current owners of the businesses you buy (e.g. will you keep them working with you and on what terms?)

^Searchfunder member might be able to help our Anonymous Poster determine the best legal setup in the UK.