I don't know what it costs to replace a 5D Mark III shutter in the UK. If the work is done by a Canon Service Center in the U.S. it runs around $320 before any discounts, such as CPS (Canon Professional Services) membership, are applied. Any applicable shipping charges would be additional (with most CPS membership levels return shipping is free - with the highest level Platinum membership shipping is free both ways). If the mirror box needs to be replaced as well the cost for both the shutter and mirror box will be about twice the cost of a shutter alone.

At least here in the U.S. it is far more affordable to deal directly with the Canon Service Center than to go through a local Canon authorized dealer who usually just ships your camera to the Service Center for you and doubles the cost of your repair. There are a few Canon authorized service centers (not owned by Canon but their technicians are certified by Canon) in the U.S. as well.

The there's the DIY method that is not for the faint of heart. This article is for a 5D Mark II. The 5D Mark III would be similar but many of the specifics would be different (location and number of screws, ribbon cables, etc.).

Many 5D Mark III bodies go well beyond 150,000 shutter actuations before the shutter needs to be replaced. Of those reported to Oleg Kikin's shutter life database, the average 5D Mark III with a good shutter has 221,628 actuations on it. Of those reported to have failed, the average was at 187,379 clicks. Note that such a survey usually includes a disproportionate number of failures, as those who have a failed shutter are more likely to look for such a site. The Kaplan-Meier estimate applied to the numbers from the submitted reports for the 5D Mark III indicate you have a better than 3 out of 4 chance of making it to 500,000 shutter actuations before it fails.