Just in case this is helpful to anyone! My son failed his test on 11 June. We rebooked straight away and earliest was 16 Nov which he booked. He then registered with the website and app in the photos, about £20 each. They ping the DVSA database every 5 mins for cancellations (so two will ping at different times increasing your options). Between the 2 we got offered around 6 increasingly earlier cancellations and decided to keep searching till we got August. Less than 24 hours after rebooking we got 1 July (thankfully he passed today). You need your settings to auto accept what is offered or you’ll miss it. Once it finds an earlier date and auto accepts it stops searching but if you want to keep trying, you reactivate (all for the same fee) and it keeps on searching. So book anywhere but set your cancellation search to only your chosen test centre(s). It updates the DVSA for you.
My son is starting an apprenticeship in August and being able to drive there is 30 mins whereas public transport is 3 trains and foot because of awkward location. So whilst it’s more money spent, this service has been a lifesaver.