Is there a preferable time of year when one should apply for a PhD in the UK?
Question:
Is there a preferable time of year when one should apply for a PhD in the UK?

Answer:
This very much depends on the university, programme, funding, etc. So it's hard to generalise a single "preferable time".
But, that being said, many STEM programmes (which are not on a rolling admission) and funding opportunities tend to have application deadlines between around mid-September and around mid-February.



Question:
Does one lessen one's chances of acceptance if applying nearer to the official early summer deadlines?

Answer:
Not unless it says somewhere that places may be filled before the application deadline.



Question:
Should you apply without the BA cert and just say it is in processing (without going into reasons why)?

Answer:
Typically, applicants are not required to submit proof of any qualifications in the early stages of the application process. They are required, however, to submit an official academic transcript.
It is only in the later stages of the application process, e.g. after receiving a conditional offer, that applicants have to provide supporting documentation as evidence for meeting each condition of the offer.



My advice is that you get in touch with the admissions office of the place you are applying to, and ask them directly about the details of the application process and your BA cert.