Okay, some more information. I tend four gardens sited on very stony, very well drained ground in Shropshire. The area is a moraine, stuff left behind by a glacier, and I have literally taken tons of stones away over the years.
There has never been a puddle in the gardens, no matter what the weather, so I can vouch that drainage is not the problem. Now I understand that a better lawn treatment regime would help matters no end but I've never had much luck with that. All my fault, I know.
The gardens are not overly large, the biggest about 1000 square meters, but they are complicated by beds, rockeries, trees, curves and corners. This makes, for instance, mowing awkward and, after trying many sizes, have settled on a simple push 18" jobbie. I tell you this so you can envisage that I can't use a spinning spreader on the lawns.
I have tried spreading fertiliser and such using a drop spreader but never get it right. The last time I tried it I ended up dumping much too much where I stopped to turn around.
This is why I decided that liming the lawns, if I can get that right, would help combat the moss on the principle that moss likes acid conditions. I have tested the ph of the ground and it is on the acid side. I don't understand quite how hedgesparrows old gardener got his great results using peat and grit, but there you go....
This is going on bit, ain't it? I have found over many years that in this area the only scarifiers on hire seem to be combi machine, sort of slitters and rakers. Not too good. I have to drive about 12 miles to hire the Bluebird and this does get out the truckloads of thatch that tinbercutterdartmoor mentions. The Bannerman is probably the same sort of machine.
I have been hoping that the Viking scaifier would prove good because I can pick that up for less than 500 quid. I've looked at it in the shop and it is very light and mobile - would get round the obstacles without problems. I can't justify much more.
I'm very grateful for your replies. Hope I haven't bored the pants off you all.