Moss only grows on soil and surfaces that are constantly moist and are poorly drained. So no amount of chemical treatment or special 'tools' will adequately change the situation. It is clearly worse this year because of the constant wet weather, but a long term solution for lawns or borders would have to be improving drainage. In the borders, you could try working over them in the spring and incorporating grit and gravel, but if the underlying water table is high, this won't do much in very wet weather.
Sorry.

If you turn the moss over completely to cover it and then hoe the top soil weekly the moss should largely be eliminated because the top of the soil will be crumbly and will dry out quicker so the moss won't be able to grow in the dryer soil.

Agree with Bertiefox and Anchorman. I would fork it into the soil, thereby incorporating it in the soil and aerating it, preventing it coming back.

Sounds like your soil hasn't been dug for a while - do as the others say and turn the soil over, either with a fork or hoe or something. Moss growing on borders indicates poor cultivation - it is commonly seen at the end of winter on heavy soils, but usually not so much in autumn because people turn their soil over during the spring, summer and early autumn.

Thank you for all your responses .You have me sussed I am a fair weather gardener, so the lack of motivation caused by bad weather and bad back has taken its toll . I will give myself a good talking to ,and purchase a few bags of grit and get on with it !

Are you sure that it is moss and not that 'mind your own business'? I've never had moss growing on my soil so I don't know if it generally does. My garage roof is covered with it. If it is 'mind your own business' you will have a problem.

C&G: it'll be moss - it commonly grows on heavier soils, especially in damp conditions. I turn the borders here 2 or 3 times during spring summer and autumn, but there's always moss growth in spring sitting on the top.

Basilncle: you may not need the grit in reality - you just need to turn the soil over more often! With a bad back, once you've done it properly with a fork, then get yourself a hoe or a long handled small fork and do it more often - much easier on the back.

I agree about the regular hoeing .

A dutch hoe or a long handled cultivator are both quick and easy to use once you've broken up the soil.

http://www.flickr.com/photos/31559373@N00/8106150960/in/set-72157631812964813

I've made some videos showing the use of these tools which you might find helpful

They're here

http://www.flickr.com/photos/31559373@N00/sets/72157631812964813/

My mum who is 83 and has a heavy clay soil was having problems keeping it weed and moss free. I live too far away to do it for her but I spread a 2-3 cm layer of potting compost over the surface and around her plants and now it is as easy to hoe as hoeing sand. She only hoes the top 2 cm so never touches the clay below. It looks attractive all year around,drains freely so moss doesn't grow. It will need topping up occasionally as worms will drag the compost into the lower soil but that will lighten that soil so it's an excellent and quick solution.

The area in question was a 3 foot wide border around a lawn about 20 feet by 15 feet. It only took me 30 minutes or so to spread the compost