As in, buying under right to buy?
If so 2 family members have bought theirs in the last decade. (Assuming nothing much has changed...) Initially they had a valuer come out to inspect the property before offering a sale price, inclusive of the discount you're eligible for, if any.
They should also take into account the approximate value of any work that you have done to the property (improvement wise) and deduct this from their offer.
For example, over the course of around 25 years my family member added a driveway to the property, a new kitchen etc. They took approx £15k off of their offer price for the work that had been done.
Made up numbers, but say property value was £250k, eligible for discount of £100k, value of work done to the property, £15k- offered for sale for £135k.
Keep in mind that you don't need to accept the offer they make to you if you think it's not in line with market pricing. You can ask for another valuation, a valuation from a local estate agent or you can make a counter offer, giving reasons why if you feel they've over valued it or why you feel it's worth what you've offered instead.
One family member appealed their valuation and this did elongate the process significantly. In total, it took about 9 months for a standard no chain purchase due to all the back and fourth. But it did result in their offer being reduced by a further £20k, so worthwhile I suppose.
The other one straightforward as far as i'm aware, completing quickly. The council agreed to complete in as little as 7 days or to your preferred time line. Obviously with a mortgage it's a little more complicated than that as they'll want valuations and surveys and searches, but that's normal.