Batteries can be on the AC side of your PV inverter, they then need their own transformer and inverter, which is less efficient, but usually easier to install. See here for comparisons. An AC battery also mean that if you get a grid tariff that varies over the day, you can buy your grid power cheap and store it until you need it. Historically, most PV in the UK has received FIT payments, which are based on what you generate, and putting a battery could complicate that. There are various standards and licencing rules which affect how you connect things that can feed the grid; there are others here who can explain them better than I can.
PV systems are mostly set up to switch off if the grid goes down, otherwise they are feeding live power into the grid when people are trying to fix it. Tesla batteries have a cutout that isolates the house from the mains in that situation.