The only free-to-use, no registration, no spam software I'm aware of currently, is the "100PcVatFreeBridge" www.comsci.co.uk/100PcVatFreeBridge for VAT tax returns (which are already using an early version of the MTD software). I don't think it's open source itself, but they are a supporter of open source projects. I'm hoping they'll be doing a non-VAT version. Basically you set up a spreadsheet/CSV file in a particular way, and it converts and uploads it.
As for the lack of being able to submit your tax return directly to HMRC, as everyone has for decades, and the lack of government-organised open source submission software, there is still a bit of time to ask your local MP to raise this in Parliament. Here's our government's own guidance on how and why you should always be using open source software for things which are publicly funded www.gov.uk/guidance/be-open-and-use-open-source. It would be a reasonable question why they're ignoring their own advice and instead suggesting that you ferry your personal and financial details to random (possibly criminal) companies in America to submit your tax return.