http://www.nationalr… and http://www.virgintra… for trains
http://www.nationale… for intercity buses

Taxis are expensive — not sure where you’d find rates, but if you’re a budget traveler you won’t be taking any taxis.

take a look at here, UK cost of Transportation http://www.workgatew…

I can help for London.
For travelling in London, it is recommended to get an Oyster card, they cost £3 and are basically a card to keep money on for travel, using an Oyster card reduces the travel costs greatly. You can put money on your Oyster card at any tube station and many street side shops. You can also buy bus passes or travel cards for longer time periods.

Bus(including tram):
£1.20 per journey (£2 without Oyster card)
When using an Oyster card for buses the max you will be charged is £3.90 in one day, the rest of your bus travel for that day, upto approx 3am the next day will be free.

London Underground:
Average is between £2.40-£2.70 per journey (even less if for shorter journeys) this includes changing lines as long as you remain in the underground system. £4 per journey without oyster.
They also have an upper limit the the most they will charge you in a , off peak is about £5.60 and on peak is about £7.20 but when this is reached, bus, underground and London overground will be free for the remainder of the day.

Overground/trains:
These tickets all vary for distance and location. In London from about 2.10 to £7 in places. But you can’t use prepay oyster, only if you have unlocked free travel for that day or bought a travelcard that covers that day.

Taxi’s:
Expensive, not that efficient. In London public transport is better.

Our hostel in London sold the Oyster card for only £1. Not sure how they could sell them for cheaper except that the card cover was in French. It worked as per normal anyway. Also I’ve been told you can return the Oyster card somehow and get your deposit back but we didn’t try.

also check out www.megabus.com because they have coach and train fares starting at 1 pound with a 50p booking fee. (and yes, I have seen fares this low on the website, if you check far enough in advance; the sooner the departure, the more expensive, but it’s still cheap compared to national rail and national express)

Money Saving Expert has loads of tips and strategies for the cheapest transportation within the UK: http://www.moneysavi…

Just remember when booking long distance trains that they follow airline style pricing so buying a walkup ticket will be a lot more than an advanced booking.
Cheers
Howie