Can I file US taxes for free online from the UK?

You don't have to pay US Social Security.

See the US/UK Totalisation Agreement, pages 3 and 4 (Self-employed and reside in the UK).
https://www.ssa.gov/pubs/EN-05-10199.pdf

"Certificates for self-employed people
If you are self-employed and would normally
have to pay Social Security taxes to both the
U.S. and the U.K. systems, you can establish
your exemption from one of the taxes.

If you reside in the United Kingdom, write
to Inland Revenue at the address on
page 10."

I believe under UK regulations you do have to pay NICs in the UK, depending on amount of income.
https://www.gov.uk/self-employed-national-insurance-rates

Great! Thank you. This was what I needed. Now to file for an extension until I get my certificate!

I tried the above, but it seems I need a US phone number to register.

I'm having trouble with taxes, too. Been in the UK since Feb 2018, but am self-employed. All my income has come from US sources so far. Seems like I will have to pay SE tax, even though I have NIN and UTR here.

Is this correct?

There are ways to have a cheap US phone number. I pay about $50/year to maintain a US number through Skype.

I have a cheap US phone number via Callcentric.com.  I pay $3.95 a month for it, and can get text messages, but only as emails or if I log into callcentric from here so far. They can't forward texts to a UK phone yet..

I have a cheap US phone number via Callcentric.com.  I pay $3.95 a month for it, and can get text messages, but only as emails or if I log into callcentric from here so far. They can't forward texts to a UK phone yet..

Skype does voicemail but doesn’t do texts which is okay for my needs. Should verification codes be needed they come through as a robotic voice so I have to write them down. I have the Skype app on my smart phone so calls do come through wherever I have a phone signal. Incoming calls via Skype are free of charge but you do have the option of forwarding the calls to your phone and the charges are then 2.3c/minute

Thanks everyone! I have filed for an extension and requested the certificate. I'll look into the Skype number, too. I use Skype a lot and find I need a US number from time to time.

Happy weekend!