No, it's not legal.
The General Data Protection Regulations (GDPR) apply given that you are in the UK (regardless of where the Data Processor is based). The UK GDPR is slightly modified due to Brexit, but the same principles apply.
The only plausible legal basis for this action would be that you consent to it, and you're entitled to withdraw that consent at any time.
Some may claim that Article 6.1(b) applies, i.e. that it's necessary to send marketing email in order to fulfil the contract, but GDPR is clear that bundling such consent into a contract for service simply to permit the data processor additional actions isn't allowed, as I'll demonstrate.
UK GDPR requires that consent to use your personal information (in this case, your email address) for the stated purpose be freely given.
Consent to use your information for direct marketing is not freely given if it's inseparable from the consent to use it for some other service, as per [recital 43]:
Consent is presumed not to be freely given if it does not allow separate consent to be given to different personal data processing operations despite it being appropriate in the individual case, or if the performance of a contract, including the provision of a service, is dependent on the consent despite such consent not being necessary for such performance.
And Article 7.4 gives this legal effect:
When assessing whether consent is freely given, utmost account shall be taken of whether, inter alia, the performance of a contract, including the provision of a service, is conditional on consent to the processing of personal data that is not necessary for the performance of that contract.
The intent of Article 6.1(b) is that only the processing required for the service you have bought is allowed (e.g. if you supply your address for delivery of stuff you've bought, the data processor can use that address to send you the stuff, but is not allowed to add a contract term that allows them to send you unwanted stuff).
Examples of emails that Article 6.1(b) would allow (in my assessment) include things such as notification of upcoming downtime, or a reminder that subscriptions are due, but not unsolicited advertisements for other products. There's a grey area that's open to interpretation, where adverts are piggybacked onto actual service messages.