Lecturer in Math position application - UK - Teaching statement
Having applied for jobs in both North America and the UK, I can confirm that unless the advert and "further particulars" specifically mention it, there is no need for a teaching statement.

I thought I would add some further comments, which aren't exactly relevant to your question but which came to mind since you mentioned UK vs NA.

For a standard "lectureship in pure mathematics" (presumably entry level?), I was told by a 3rd party, when I applied for my current job, that in many UK places a list of courses in the CV, plus remarks of the form "my teaching was rated in the kth decile by student questionnaires," would be sufficient.

The important thing is an up-to-date CV, which should emphasise the extent of previous teaching experience. Success in getting grants, either as a graduate student or postdoc, is probably also worth including. Other information such as conference participation and refereeing work is rather secondary; you can include it, but I don't think it would make much of a difference.

Due to the sheer volume of applications, it may be worth including things like the publication list at the end of the CV rather than in a separate document. You might also wish to highlight your four best papers in an early "Selected publications" section; sadly the spectre of REF-fability is always on the minds of committees. The CV is often what is circulated when drawing up a longlist. The research statement should probably remain separate, and is roughly speaking the same kind of thing that one would prepare for a North American application.