You need to check with gas safe but the registration and the operatives can be thought of as two different things. You can be an operative for as many companies as possible.
If you run two separate ltd companies they both need separate registrations because they are defined as different legal businesses.
It used to be the case that a company could have NO operatives but still be registered and this would be the cheapest solution.
For registration with no operatives you have to be subcontracting and your test would be that you have systems in place to ensure your subcontractors are qualified, registered, insured.
Of course your other company provedes the subcontactor - you.
Its all paperwork which ever way you do it.
It may be simpler & cheaper to stick with one company but have two divisions, so you still have one registration and one set of accounts and one lot of returns to HMcustoms & companies house...
By 2 divisions I mean trading names. You can trade under as many names as you want so long as there is no intention of fraud.