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First element of confusion is that you probably mean the VN Embassy in London, not the UK Embassy. 

Second, if you foresee having to change from a tourist to business visa to get the TRC, why not start with a business visa?  It is kind of ridiculous but Vietnam allows people to be sponsored by random companies linked to visa agents.  For all I know these companies may exist only on paper.  It seems ridiculous because it is.  If you have a business visa, it seems you can avoid a visa run and go directly to the TRC.

You don't need an apostille at all because Vietnam is not a party to the Hague Convention which sets the rules for apostilles.  You need translation and legalization by the VN Embassy. Check thier website for what you need.  Be sure that they translate as well.  The Embassy in Washington failed to do so for me on two documents and I had to do them by notarizing at the US Consulate in HCMC.  The current policy of your UK diplomatic service will not allow notarization and hence subsequent legalization within Vietnam.

Once you have a TRC you do not need any visa at all.  You do need to keep it to show if and when you exit the country because your passport will have no stamps indicating your legitimate residency.

embassy site insisted that it is a must before they can go through with the legalization process.

u cannot just change any biz visa to TRC. must be the same company sponsoring biz visa- work permit
immigrations mafia may refuse to give u TRC as that cuts their bribes 70%

the embassy site insisted that it is a must before they can go through with the legalization process. … 0residents

You may find some useful information . (scroll down to "Legalisation – Change to our services from 13 November 2017")
I think you can apply online for UK legalization.

Thaiger wrote:

u cannot just change any biz visa to TRC. must be the same company sponsoring biz visa- work permit

That actually makes sense which of course would be unusual in the case of Vietnamese immigration rules.  I stand corrected.

I'm planning to get a work permit when I come here and a Temporary residence card as well, which can only be done if I have a business visa. If i arrive on my tourist visa then do I need to get out of the country and re-enter with a business visa ==> apply TRC, business Visa or  working visa is required . tourist Visa is not acceptable.

And if I do my work permit will I need to apply for a new business visa sponsored by my employees? ==> You should contact with your company in Vietnam and get your Business Visa. Then you can get WP under they Guarantee. Your company have to prepare docs, you can not do it by yourself.