Scroll down to "What are the rules on mingling?" here:
https://www.bbc.co.uk/news/uk-51506729
My concern would be that, with everyone generally knowing everyone else within a bowls club, people wouldn't remain strictly within groups of no more than six and would tend to mingle with people from other groups.
'Mingling' seems to have become a key concern for the Government in their drive to keep transmission of Covid-19 down
https://www.bbc.co.uk/news/uk-54165362
and it's hard to see how such mingling could be avoided within the scenario that you've presented to us. (I ran the bar for a local bowls club for several years and I find it hard to imagine members keeping within groups of no more than six, while not mingling with other members too).