Can I be made redundant while on sick leave?

It sounds horrible - and I can quite understand that the last thing you want is to be hassled at home. Unfortunately, there's nothing to actively stop them doing this, though it's clearly not good practice on their part.

Yes, they can make you redundant while you're off. They can make you redundant at any time they want - the question is whether it's 'fair' or not by law. In order to dismiss you fairly, they need to consult with you and warn you about the position - hence why they're so determined to contact you at home. I suggest you read one or two of the emails and consider writing back explaining that you're signed off, and you're not up to thinking about work-related issues until you've recovered.