Several issues. One is lack of RCDs could find undetected cross-wiring - eg lighting circuit borrowing neutral from nearby sockets. Or just straight leaky appliances - an old boiler, immersion or something.
The other is the general condition of the installation: if the CUs are that old, how old is the wiring? Do you know it's sound - not rubber, not cotton, no 'green goo' (failed PVC insulation)? Earthing in place where it's needed?
For something of that age you might be advised to commission an EICR (£100-200) and get the system tested. Testing is part of the CU change anyway, so it's work that needs to be done (although an electrician should retest once the CU is replaced).
Having done an EICR it's essentially a todo list of work that needs to be done, and you can then show it to people when you're asked for quotes. It puts them on more solid ground than quoting for a CU change, taking it apart and discovering wiring issues that make the job much bigger. It may result in lower quotes if it means they need allow for less contingency since the job has lower risks. It may also allow you to fix more things on the EICR while the electrician is on site.
Theo