There’s no excuse for a tenant not allowing you to do a viewing while they’re still there: it’s in the Tenancy Agreement, it’s a necessity to avoid void periods, and (not surprisingly) the new tenant (who turns into the old tenant) wants to get into the property before anyone else…
However, this is much harder to enforce if, over the last month of the Tenancy, they are ill, have personal issues, or keep cancelling on you. Offering to work around the tenant is all you can do.
“I’ve got mumps and it’s infectious.” Send an agent who’s already had it.
“There’s boxes everywhere.” Good, it should be easier for the viewer to imagine their own stuff in there.
“I’m working overtime.” Not a problem, any agent worth their salt will do viewings before work, after work, and at the weekends.
Shelter says “Landlords have a legal duty to get all gas appliances in their properties inspected on an annual basis. If you are a tenant, you must allow a Gas-Safe Engineer access to your accommodation to carry out safety checks and, if necessary, repair work. Your landlord should give you adequate notice of the gas safety inspection.”
Ultimately, you cannot force entry into a property for any reason, be it to try and comply with the law or otherwise.
As a Landlord, all you can do is act in good faith, with good intentions, and using industry-recognised ‘best practice’, and you’ll probably still end up defending yourself.
Therefore, keep all records of contact with the tenant for use in any eviction proceedings (if you can’t do a gas safety certificate, you MUST evict them to get it done), or any loss-of-earnings claim against their deposit.
Ultimately, a strong & healthy relationship with your tenant is worth its weight in gold to try and avoid these problems. Be respectful, empathetic, and understanding, but make sure you protect yourself by keeping a neat & tidy record of everything because ‘he said, she said’ will not protect you when you’re facing an unlawful eviction claim.