OP, I hope you've got the message that you need legal advice.
But just to give you some idea of timescales-
As soon as the Section 21 ends, you can apply to a court for a possession order. You will be given a court date, which will be a minimum of 4 weeks away, but in reality, in most areas of the country, you will have to wait for at least a few months.
If the Section 21 is not valid, then you will not get a possession order. You can use the guidance here to check if the Section 21 you have issued is valid: england.shelter.org.uk/housing_advice/eviction/section_21_eviction/how_to_check_a_section_21_notice_is_valid
Because they've been in the property for so long, some of the things people are saying may not apply- such as the guidance about deposits, gas safety etc. But you do need to find out what is going on with the deposit, as you may need to either protect it or return it to your tenants.
If the Section 21 is not valid, then there's no point going after a possession order. But let's assume it is.
If you get a possession order, a date for possession will be given. This is usually 2 weeks after the court date, but if your tenants are in hardship, it could be as long as 6 weeks away. Tenants can also appeal the possession order if they think a mistake was made (e.g. the judge said the Section 21 was valid, when it's not).
The date on the possession order is still not the date the tenants will have to leave. If the tenants don't leave by this date, then you can apply for bailiffs to evict them. The bailiffs will give about 2 weeks notice of the eviction date to the tenants. Do be aware that at this stage, the tenants have nothing to lose so may cause damage to the property or sell your goods etc.
Anyway, the absolute minimum time you would have to wait is eight weeks from the end of the Section 21- but realistically, based on court dates, availability of bailiffs, if the tenants can prove hardship, it could end up being more like 6 months. If you've got the section 21 wrong, then you need to sort the issues, reissue it, wait the two months, and then start the process, so at least 4 months, but again probably a lot longer.
I'm not commenting on the rights/wrongs here, just trying to explain the legal process.
BTW, if the Section 21 has already run out, then you have 4 months to apply for the possession order, or you have to start again.
The only place where the financial situation of the tenants matters is whether they can prove hardship or not, and delay the process for a further 4 weeks. If you have not followed the law, and filled in all the paperwork correctly, it will cause significant delays.