Due to being unable to remove the plastic steering column cowl (long story see page 3 of this if you're interested ) I came up with the following approach to replacing the ignition switch barrel without taking off the cowl, indicator stalks and steering wheel. It's a bit tricky but it works; like keyhole surgery.

You need to obtain a length of that plastic strapping tape that's used for bundling large packages together and also a piece of rigid PVC that can be cut to make a short 'blade' I'm using a piece of 10 x 16mm mini-trunking.

You still need to remove the plastic 'pizza slices' at either end of the fabric shelf/dashboard and let it drop in order to obtain access to the cowl's underside and the ignition switch casing within.

Take the plastic strapping and roll about half its length up into a small roll, hold together with some tape and then apply heat to it for about two or three minutes, remove the tape and the strapping tape will have curled up nicely.
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Insert the curled up end of the strapping into the cowling and you should easily be able to get it to wrap around the ignition barrel housing and be able to get the feel of it and the space available to work within.

Take a small 'L' shaped cutting (4mm wide) of the mini-trunking and bend the shorter side over on itself, place this about half way along the strapping tape's length and then bind the two together using insulating tape. When applying the insulating tape, stretch it whilst binding it around the strapping to be sure that the plastic 'blade' that's now been formed is well held into position, the 'blade' should be in the centre of the strapping tape so that when it's being pulled against the barrel release catch it doesn't slide off to one side and lose its full effect. I tried superglue as well as the insulating tape but the glue didn't have any benefit. The blade should be 4mm wide and about 12mm long, this worked for me; you're trying to replicate the blade of a screwdriver that would normally be used for this task.
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Before proceeding, get to know roughly where the slot containing the release catch is by referring to AndyReact's last image in his post, also have the new barrel with its key inserted close by when ready.

Insert the key into the ignition and turn to 'Mar'. Whilst viewing the barrel housing from below the cowling insert the strapping around the barrel housing and gently manipulate it until the PVC 'blade' is felt to go into the slot containing the release catch, once you feel it go in pull firmly on both ends of the strapping whilst rotating and pulling the ignition key to release the barrel; insert the new barrel with key whilst you still have the tension on the strapping keeping the release catch open. Be careful to ensure that the new barrel is aligned the same as the old one when inserting it so that the two lugs on its end are aligned with mechanism within the housing.

I don't know which position the key was in when the barrel came out as I was doing it very quickly, nor do I know if it matters if the release catch has to be open to enable the new barrel to go in as I wasn't taking the chance by releasing the strapping until the new barrel was in.

You may have many attempts before you're successful in releasing the barrel and may need to readjust the 'blade' each time. Mine worked with the second attempt, do not rush it and take your time.:)