The cheapest will be a good tyre dealer, and some of them have first class alignment equipment these days. It may not be all that expensive to get it measured all round, i.e. castor, camber and toe at the front, camber and toe at the rear, and the printout will also show "thrust angle" which is a measure of crabbing, and probably king pin inclination and a few other things too.
Once you have that, you can then think about whether any item needs correction, but at the very least get them to set the toe. They will not know how to set camber and rear toe, unless they are a genuine Mini specialist, but you can do that yourself, with assistance from the forum if needed.
Please be sure that ALL parts that may be worn or due for replacement are fixed before having a geometry check, as worn bushes, bearings or ball joints make the check a waste of money, as it will need to be done again when they are fixed.