Yes Richard do it asap and spread the compost. I would normally recommend spreading manure or compost before covering ground with plastic, so worms can then be busy and break it down while the ground is covered, creating a better tilth – always as long as the soil is moist at the time when it is covered.
More generally, I think that once soil is clean of weeds (apart from occasional annuals) there is no advantage to covering with polythene, instead put on a 2" mulch of compost/manure in autumn. Pull any weeds that grow over winter, knock the lumps out with a rake or fork in any drier winter weather (I was doing that today), and by March you will be ready to sow and plant.