I need to buy a new bike as my old one is too small...?

The most reputable firm i've heard of is Raleigh and I'm suspicious of other makes if I haven't heard of them - which other makes are good?
Also which type of bike to buy - I will be going on roads, bumpy tracks and across muddy fields so it needs to be comfortable for the bumpy tracks.
I'm about 5'4/5'5.

There's a lot of other good bicycle manufacturers besides Raleigh. There's Trek, Bianchi, Cannondale, Specialized, LeMonde, Giant, Fuji, Felt, Jamis .... the list goes on and on.

Go to some local bike shops and look around. Tell them what kind of riding you intend to do and what your budget is. But don't expect to pay a department store price for a good bike.

From what little you've said in your question I might suggest a hybrid bike. That's a cross between a road bike and a mountain bike.

The most important thing is getting a bike that fits properly. That's something a good shop should be able to do.

By the way, try Googling some of those bike names. They all have websites for you to look at their products.

Claude Butler is a well known quality brand and would recommend to anyone, so is the brand Dawes. If you are going to be cycling on the road i would recommend you to buy a bike from Claude Butler called an Urban, there are lots of styles in that range, at different prices. The quality varies on what you are willing to pay.
A 26" wheel would be ok for you.
Have a look on the website www.falcon.co.uk and follow links to the Claude Butler range.

I have a Giant road bike and a Trek mountain bike..I love them both because they fit my body and meet my needs. I also believe fit is more important than the brand. Visit a few bike shops, have them fit you, test ride some of the bikes and do lots of internet research. Take your time finding a bike you can love and enjoy riding. The reputation of the bike shop is just as important if not more important than the brand.