It makes much more difference for certain professions where accreditation is required or useful in progressing in that role.
For example, not having an accredited engineering degree means you won't be able to aim for CEng status, which is actually useful in progressing in an engineering career. Equally for becoming a biomedical scientist in the NHS, you are required to have an IBMS accredited degree, as well as to register with the HCPC. Without an IBMS accredited degree, if you wanted to work as a BMS, you would need to get your degree validated by the IBMS, and would likely need to either take top up modules to meet their accreditation requirements, or you would need to do a whole new degree if it's not got enough overlap.
So, accreditation does matter in some areas, and in particular it matters in the areas covered by that degree programme, unless you just wanted to go into academia (i.e. do a PhD etc) or work in non-engineering, non-BMS roles (e.g. as some kind of lab scientist otherwise in industry). Or if you just want to get some random business/management/financial services grad scheme role, where they don't care what you studied at undergrad.