Covering part of a plot with a weed surpressing membrane is common advice to gardeners tackling an overgrown plot , and makes particular sense for traditional diggers.
In my mind it might also make sense to non-diggers if they don’t have access to enough compost to cover the whole plot in their first season and/or are initially unsure as to how much of the plot they want to bring into cultivation – it’s very easy to end up being swamped with veg!
Depending on the type of weed and the eveness of the surface an alternative to covering with membrane might be to use a lawn mower to mow any uncultivated areas, giving you a source of “green” material to compost for your next beds…
Good luck!
CP
(also on clayish soil – for which I must say I find Charle’s no dig approach works supremely well)