Re:
If the ground's waterlogged, it may because it might be compacted below the soil surface, where a 'pan' could be forming underneath. A pan is a crust which often forms when ground is always dug or rotovated to the same level or where the water table sits. In the old days, people would 'double dig' plots – a real killer of a job. It depends what kind of soil you have – we're on heavy London clay. Had this problem with large parts of our plot, which has deep seams of clay running through it. It's like the Somme in winter and in summer it sets like concrete with deep fissures running to the centre of the Earth. It was hard slow work, but basically had to use a fork to crack through the pan and deeper, roughly turn everything over, add sand and grit, then mulch heavily with manure to leave for a while.
Rotovating might make matters worse. If it's light machine it might bounce off and skim just the surface creating a fine 'soup'. A heavy machine may get bogged down and make compaction worse. Hiring one may end up costing more than the £50 quoted by the council. Mind you, if you've already planted stuff, I wouldn't trust the council or contractors to not plough through planted areas.
Best option, if you're back is up to it, is get some bags of grit and enlist some friends to help steadily dig over, especially if it's not you in particular the council is targeting and no real rush to cultivate it 'or else'. The £50 could provide some of the catering or beer money.
Btw, which council is it?
