As Tod says and if you can get a letter from your embassy that could also assist, but ultimately you're at the mercy of the IO looking at your application. Show respect and wear long pants - it might just sway it
Brighton Shanji. As you were previously on a non-immigrant visa you are no longer eligible for covid extension. You should either try to find another non-immigrant visa to move onto, or do a Phnom Penh visa run if you want more time in Thailand.
Sa Bari. You can most certainly APPLY for a further extension. Whether it is granted or not is at the discretion of immigration. Not everybody gets one, so it's a hit-and-miss scenario
If you're still on a tourist visa/visa exempt there's been no defined limitation, except at this point you have up until March 25 to apply. The concession may/may not be extended past this date. That depends on the mood of the government a day or two before that date.
If you entered on 30-day visa exempt basis you can visit an immigration office and extend a further 30 days, which will give you the 60 days required. The cost of the extension is 1900baht.
There is no such beast as a 45-day visa/visa exempt.
Marco Filippini. UK is visa exempt, so no visa required and no additional form to complete. Along with all arrivals to Thailand you will be given an immigration card to fill in on the plane.