Okay, let’s go deeper down this rabbit hole
There are different ways of classifying consonants. One of them is their place of production, e.g. dental, alveolar, labial, etc. Another defining characteristic is their way of production: plosive, affricate, sonorant, fricative, etc.
The British /θ/ as it is taught in the video you linked is indeed a dental sound, however it is a dental fricative sound. Fricative sounds are , obviously enough, sounds that involve friction in their production, e.g. /s/, /f/, /v/, /ʒ/, and, yes, /θ/. They are radically different from the so-called plosive consonants (aka stops) in that they do not feature a single release of a blocked air stream . Good examples of plosive sounds are the Sinhala /p/, /k/ and the Sinhala dental voiceless plosive /t̪/ (it is indeed a dental voiceless plosive as you can see here).
Summing it all up, the British /θ/ and Sinhala /t̪/ have the same place of articulation but completely different modes of articulation. Other similar examples include /b/ and /w/ (here you could consider the development of ‘vv’ to /bb/ in Pali, which may be a sign that ‘v’ at some point was pronounced as /w/), /k/ and /x/ (here you make consider the phonological development in the German macken /makn̩/ > machen /maxn̩/), etc. Put even more shortly, /θ/ and /t̪/ are two different sounds.
Just in case, using approximation when speaking a foreign language is totally okay, this is a legitimate way of struggling with a foreign phonology. I do it all the time when I can
As the Pali consonantal inventory does not even feature a voiceless dental fricative (or, for that matter, neither does the Sinhala consonantal inventory) and /θ/ and /t̪/ are different sounds, the traditional Sinhala Romanization of /metta/ as meththa is erroneous and misleading.
Anyway, compared to how the Americans butcher Russian family names such as Gurdjieff in their pronunciation, it is a merely trifling thing, but I would recommend avoiding it in the future in any possible context.