The material for an MK2 Cooper S is black vinyl called MG Black. Its available for approx $20/ per 1m x 2m lenght from most trimming supply places. So approx $10/square metre. Get the slightly more expensive variety of "MG Black" as it is only a few bucks more and is much better. Your trimmer should have no probs sourcing this material and they should also be able to get the correct rubber diapraghm (which is also available from most mini places). Just keep the prices for those items in mind incase that the trimmers charge you too much for them.
Then take your low backs to a selection of trimmers and get quotes from those who look like they know what they are doing. Go with the best quote/most experienced looking guy. You can always refuse to pay and demand they redo it if the quality is not what was promissed.
Alternatively Newton Commercial (
www.newtoncomm.co.uk) offer all retrim kits for the front seat base and squab (but in the UK MK2 Cooper style which has a different pattern of lines) but you still have to know what youre doing to install them on the seat. Plus they are usualy pretty expensive and you'd still have to get them shipped over.
One advice though - Get the trimmer to strip and repaint the metal skeleton and fittings or do it yourself or your brand new retrimmed seats would still look dirty and rusty.