Good news. From the 25th Sainsbury's will start accepting contactless and Apple Pay as well as Android pay, both of which will not have the £30 limit.
Initially it will only be available via a select amount of 'Local' stores, I.E. all those that have the new till system update, usually this means stores with self scan machines will not be in the initial roll out. A good way to determine if your local 'Local' store has the new update is if when you pay on card and you get the receipt, if the card verification and the item list is on one receipt instead of 2 separate ones then the store has the new till system update, bare in mind stores are being updated daily.
Supermarkets should get their roll out from early 2017.
Since the roll out is starting now and will then be on an individual store by store basis it is unlikely that I will be able to provide anymore information on this in future.
Pay at pump facilities in petrol stations will not have contactless, but the petrol store kiosks should.