Prices quoted are for a 2008 full price adult ticket,
checked at the time of writing.

This one is a bit of a no brainer. There were a couple of alternatives I considered such as Oakwood and Flamingo Land which are both good as cheaper alternatives as parks, but their location a long distance from Alton Towers means they're not really viable alternatives unless you're located locally to one of those parks.
Drayton Manor is reasonably close to Alton Towers, is cheaper and even has a nice line up of new family rides for 2008 in the form of Thomas the Tank Engine Land, which does make it worth checking out.

I'm not really sure Blackpool deserves to be on this list, as although it's expensive, compared to other big parks it is priced on a more reasonable level. Especially if you avoid it on a peak day.
Locally your main alternative is Camelot, a park I can't believe Merlin don't own. I didn't choose this though because I thought it would be more appropriate to choose a seaside resort to match Blackpool as a location for short break, which gives me a little more flexibility in terms of location.
With Fantasy Island, Skegness current prices I can't really recommend it as a cheaper alternative. Pleasure Island in Cleethorpes did strike me as a possibility. Another one would be Oakwood, or more accurately Tenby, a coastal resort a short distance from Oakwood and Folly Farm.
In the end the choice was obvious. In terms of park feel, and resort attraction Great Yarmouth was clearly the choice to make as an alternative to Blackpool, with it's wristband being cheaper, and Joyland also offering better value than the South Pier.

Brighton Pier should be the park I visit the most. I think it is just about, but the steep prices do put us off from visiting that often. Luckily we are spoilt for choice in alternatives available along the coast.
There are small family parks in places such as Dymchurch, Hastings, Eastbourne and Littlehampton. They all offer alternative days out as resorts, but there parks are for a younger market than Brighton.
The park nearby that offers the best alternative as a park is Funland, Hayling Island, with a set of rides that comes close to matching Brighton, at a cheaper cost of wristband. The problem here there is limited stuff to do in the Hayling Island resort as a whole compared to Brighton.
That makes my final choice Clarence Pier, Southsea. You could argue the lack of wristbands, but with some of the good deals on tokens you can do all the rides you want for about £10 per person, and I don't think I'd end up doing that many more rides at Brighton, even with unlimited rides. The rides here don't quite match up to Brighton, but come up to a good level making the value for money better, plus there are attractions nearby in Southsea, and a short journey away in Portsmouth, that makes it a good alternative for a day out.

This one seems pretty obvious at first. Adventure Island isn't that far from Chessington and offers a good set of rides, aimed at a similar market at a cheaper price.
My slight concern is that Adventure Island won't provide the full day out that you'd expect from Chessington. To be fair a lot of this is due to the generally shorter queues, and the fact the rides are in a more compact space. My concern here is that paying for alternative activities such as the arcades and the Aquarium can offset some of the savings you make.
If though you're willing to accept a shorter day, or spend some of the day just relaxing on the beach, or window shopping on Southend High Street, or the nearby Lakeside Shopping Centre, then it makes a good alternative.

Looking at the list Paultons Park is one of the most attractive alternatives in terms of offering a better deal than its more expensive counterpart. £35 is a very steep price to pay to get in to Legoland, making Paultons Park costing less than half that a very attractive alternative.
Paultons Park main roller coaster the Cobra I think is better than any of Legoland's coasters and the rest of the rides also match up well to Legolands attractions.
The main advantage Legoland has is in the theming, but I think the animal collection at Paultons Park is a good addition that does offset some of that advantage in terms of park appeal. At the current full prices I would sooner visit Paultons Park over Legoland.

I think this is the one I struggled with the most, as their aren't really any cheaper alternatives aiming pacifically at the teen and thrill seeker market like Thorpe Park has.
I think I still need to choose one that does a good job of catering for thrill seekers. Oakwood and Flamingo Land both cater for this market well, but both do have the problem of being too far away to be considered an alternative.
One I did consider for a while was Funland, Hayling Island. It's not to far from Thorpe Park, and has a good selection of rides for thrill seekers.
In the end I chose Drayton Manor for a second time. Although it mainly aims at the family market, it does have a good selection of thrill rides and a couple of thrilling roller coasters, plus the water rides and some of the scenic rides aren't to kiddie orientated either. My slight concern is that at just under 100 miles from Thorpe Park it may be a bit out of the way for some visitors to Thorpe Park, but of all the parks within a 100 mile radius Drayton Manor is the best one you could call a cheaper alternative for the thrillseekers market.