BUSES

It is possible to get a bus from London Victoria - to Granada.
The price is 104 pounds (or euros it is not clear) .
Info here:
http://www.eurolines.co.uk/coach/

TRAINS

The journey consists of the following.

Get a eurostar to Paris
http://www.eurostar.com/

Cross Paris and change stations from Gare de Norde to Austerlitz.
Get on the Paris Madrid sleeper train.  

This is the website of the company who run it.
http://www.elipsos.com
At the moment they have a special offer of only 71 euros.

Get from Madrid - Granada either by bus or train.

To go by train go to Atocha Station  
This page has the train info
http://renfe.es

To go by bus go to Méndez Álvaro Station. (it's on the underground)
This page has the bus info
http://alsa.es

OTHER IDEAS:
If you don't like the idea of the sleeper train get a fast train to IRUN on the Spanish border and spend the night or a couple of nights in San Sebastian or go via Barcelona.

There is a high speed line from Barcelona to Sevilla.
Spend a couple of nights in Sevilla then get a train to Granada.

BOAT AND DRIVE
You could get a boat from Portsmouth to Bibao
http://www.poferries.com/

Plymouth - Santander
http://www.brittanyferries.es/

It is fairly easy to drive from the north coast of Spain to Granada in one day.

BOAT TO FRANCE AND DRIVE
I have done this journey several times:

To cut down on the driving you can go to CAEN then go straight down.
To cut down on the ferry price you can go via Dover to Calias or Boloungne.

To get to Calais from Granada you normally need 2 nights in a hotel.

On previous trips
When coming down from Calais I have stayed  just north of Bordeax first night and  near to Burgos on the second night.