I follow pots with green manure, to a)scavenge minerals & nutrients, b) prevent leaching during winter and c) provide composting bulk, (I hate bare ground!). However; depending on the weather, early spuds could be lifted by late June, giving plenty of opportunity for another crop. I couldn`t plant climbing french beans that late in East Yorkshire so would probably try dwarf bean plants (that have been started in the greenhouse or frame), lettuce or carrots.
Cheers
Pete