I'm surprised you weren't aware this was a risk when you decided to rent out your family home? Didn't you research the pitfalls or ask the agents about anything that could potentially affect you in the future?
I looked into letting issues back in 2003/2004 and decided against it, not least because of the potential financial risks associated with an illiquid asset, or the social responsibility of providing a home for someone - ie would have felt bad about just kicking them out of their home because it suited me.
When I asked about the service provided by letting agents and their insurance against tenants' non-payment of rent I was advised that the only instance the insurance wouldn't pay out was if the tenant was advised by the Council to stay put after a Section 21 was issued.
Clearly I researched further and found out that it can take nine months to resolve the issue - and nine months of the rent not being paid in some cases.
More than a risk I'd be prepared to take on. However, lots of people have piled into buy to let saying they were prepared to be risk takers and you've got to "speculate to accumulate" mentality. I assumed they'd all researched all the angles and understood this risk and financially factored in voids, tenants not moving out just because a S21 is issued.
Most people on this thread also seem to be aware this has always been the standard advice for tenants from the Council too.
Five years ago a friend was given this advice when her landlord returned from New Zealand ie" find a new home pronto as I want my house back". Turns out issuing a Section 21 is just a request and the Council will tell the tenant to stay put and not to make themselves homeless. Providing a home to someone because it suits you financially at the time comes with risks.
When letting a property a large pot of emergency money is required to be on hand for such potential situations. That's the risk for the reward of potential gains.
Hope the tenants find something suitable, but I wouldn't expect them to jump and find a new home immediately just because it now suits you. Investments come with risks. It doesn't matter that you don't consider yourself to be in it for the money etc - fact is you are - they paid your mortgage for you and it suited you financially at the time, and now you want them gone. You became a landlord when you let your property and you need to take it on the chin and say that's the risk I took.