Given their use of terminology, it looks like that UK ANSP has demonstrated an unfortunately poor understanding of the situation.
In the EU, Part-ATS has essentially transposed PANS-ATM into rule, AMC and GM. Those rules sit alongside those in SERA to create a ruleset for ATS provision. EU ANSPs will then develop a manual of ATS (that won't be referred to as a MATS Part 1) to put that ruleset into an operational context. Importantly, most EU countries will have one State run ANSP so have one manual which will be supplemented by local instructions at each ATS unit.
In the UK, we do not have the same content in Part-ATS as the EU; we left the EU before they came into effect. Our operational ATS provisions are contained within our MATS Part 1 (CAP 493) which is published by the CAA and is complemented by local unit instructions contained in a MATS Part 2.
As a general statement, our MATS Part 1 provisions are aligned with PANS-ATM but there are some differences. Notably in how we provide services in class G airspace. In controlled airspace, they're about 98% identical.
Does that help?