Firstly, the relevant legislation is now the 2010 Equalities Act.
Yes, if you're taking insulin, you should test and an employer should make reasonable changes to allow you to do this.
I'm trying to understand how testing is 'inconvenient'. It doesn't take very long to do. Is this person maybe a bit squeamish about small amounts of blood?
Is there a valid reason not to test?
I can see it might be inconvenient for an individual to test if, say, they were working on a food production line, or other sterile or semi-sterile environment where it might involve more than a moment's distraction, but provided the Employer can be helped to see the way forward, by whatever means, it doesn't seem at all unreasonable.
I think it would also be worthwhile asking, politely, what "inconvenient" means to the employer in this context. Again, if the OP is using a clocking on and off, with breaks needing to be clocked off, it could be an inconvenience if there are several additional off/ons in the day to be accounted for, if the system isn't automated.
I have no idea what work the OP actually does, these are just potential examples as thought starters.