Velo Club Cumbria run a very successful Time trial league from April through to September with club events normally held on a Tuesday night. The leagues are arranged on ability to allow everyone to be in a competitive group. In addition to this the club has end of year awards including Club Champion, Best All Rounder, Hill Climb Champion, Fastest 10, 25, 50 mile TT (can be set on any course) and most improved.
In addition to the club events many members take part in the lakes and lanc SPOCO series http://www.lakesandlancsspoco.co.uk/ and also the North lancs TT https://nltta.org.uk/
Tuesday TT League details - https://docs.google.com/spreadsheets/d/1ukpQRdhXTLMQRz43kb_e2SutW_L96FAHm6D-k4-RcWs/pubhtml