No, you don't have to have your own building. If you can get a school hall it can be adapted to the demands of the Litugry with a bit of furniture removal. In some senses it can be easier than an Anglican Church with a high altar.
Where two or three are gathered together - and a roof can be had (as a concession to the British climate) then we can be away. Of course, without a priest there is no Eucharist, but it is possible to have the other services - for a long time there were three of us doing the Evening service in Suffolk.
Best of luck with your endeavours.
In this is love, not that we loved God, but that He loved us and sent His Son to be the propitiation for our sins. (1 John 4:10)