If the seat pan edges are good, the foam is not out of shape, and you are careful, installing the cover is not hard. The chrome strip is easy.
You may find that the only option is to have an upholstery shop make you a cover. Here is part of a post from Wassell:
"If you have been searching for seat supply for your vintage British motorcycle as of late, you may find that many of the best-selling seats have been out of stock with many suppliers for months now. There have been some contributing factors that have left the supply chain in peril, including a general economic malaise in Europe, a closing of a major supplier in the UK, and the absence of a manufacturer of “pressings”, or seat pans.
We have used three different suppliers for seats in the past, including RK Leighton, P&P Seating Ltd, and Wassell Ltd. P&P Seating was a supplier of premium-grade reproduction seats, and once was one of the biggest manufacturer of seats for vintage BSA, Norton, and Triumph motorcycles until they closed in early 2024. We have also stocked the Wassell line of economically-priced seats, which sold well and offered a reasonable alternative to the premium-priced seats from P&P and RK Leighton."
Wassell no longer sells Norton or Triumph seats and the only BSA seat they have is for a Bantam. The Bonneville Shop has seats and covers but they list them for as right for all 850s (I don't think that is correct).
https://www.thebonnevilleshop.com/p...m-and-sprags-pn-06-3676-c-60-0697-tbs-4340-r/ Their complete seats look nice and fit just OK but they don't have them for MKIII AFAIK.
Best I can tell, R K Leighton is still in business - I don't know if they sell to end users.
info@rk-leighton.co.uk You could write them and see what they have to offer.