Can't remember what sort of sheep you have, TL. When will you tup? When do you plan to sell the lambs?
If the lambs are nearing the magical 38-42kgs liveweight, and you're not wanting to tup in the next month, I'd say just sell them off their mothers as soon as they're fit enough to go. Less stress all round.
If you're not tupping soon, but the lambs need longer to finish, one option if you prefer a more natural weaning is to give the lambs a creep area and feed them cake there, while keeping their mums on poorish ground and not giving them any cake. The mums will dry off themselves and the lambs will become more self-sufficient - especially if you can arrange it that they have access to better grass via their creep area. One day you can just shut the return-to-mum route off and they'll hardly notice.
If you do want to wean soon, it's total separation and steal yourself for 48 hours of blaring from both mums and lambs. Put the mums on poor ground, leave the lambs where they were for the 48 hours, then give them a mineral drench and move them onto good grass - usually it's 'fogs', where a hay crop has been taken a few weeks ago, for the lambs, but in the current weather you may not have any fog available.