Question on repos

I agree that it is a tricky bit to fully understand. As you say, the repurchase price is set, and the repurchase of the gilt would not normally be described as "cash settling the gains and losses". If a gilt on repo is being rolled indefinitely, then there is something that could be described as "cash settling gains and losses".
On the day that the repo is up for renewal, the gilt would be bought back at the prescribed price. the cash would be raised by re-repoing the gilt in a new repo arrangement on the same day. If the gilt has not moved in price, this should not cause much of a cash issue. If the gilt has fallen 5% in price by the maturity date, the re-repoing of that gilt would bring in too little cash to buy back the original gilt at the pre-arranged price. thus the "gain or loss" would result in a cash settlement issue, as the balance of cash would need to be found. Fortunately as repos as collateralised, the cash should be sitting in a margin account somewhere.