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 Parishttp://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 infohttp://renfe.es
To go by bus go to Méndez Álvaro Station. (it's on the underground)
This page has the bus infohttp://alsa.es
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 - Santanderhttp://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.