As far as I'm aware universities don't permit you to be enrolled at another institution simultaneously as a matter of policy.
Note the OU has an "Open Degree" programme where you can combine more or less any subjects and modules offered by the OU. This may permit you to take a more bespoke degree while still studying at the OU as you intend.
There are also as alluded to some more flexible combined study schemes noted above. Without knowing what subjects specifically you are wanting to combine (knowing why might also be helpful to guide advice but less essential than the what) it's harder to offer advice about it.
Note also the term "dual degree" in the UK has a specific meaning and is very uncommon. It's not the same as a joint/combined honours degree. This is also why it would be helpful to know what you want to study (and ideally, what your goals for that are) as it may be there are existing programmes that would cater to it but that are labelled in a way you hadn't been looking at.