So I had a closer look at something.
There is no birth registered in the surname Gurzhii in England or Wales. None at all - not just for around the time she's born. Thats going to potentially complicate matters too in terms of paperwork. Just because Iullia is on the electoral register doesn't mean she's a UK citizen. You can be on it if you have residency because you are eligible to vote in local elections (but not general elections).
Clive may well be - hence going to the UK Consulate for help because any child of his would be eligible for UK citizen. But nothing here to say that Iuliia is definitely a UK passport holder and that might make things complex depending on their paperwork.
Iuliia may well be married to Clive. However this doesn't mean that she's a UK national though. She may just have UK residency. And actually, I'd wonder if they had marriage certificates with them. Given that it looks like she never took his surname, I have to say that might complicate matters - I've certainly found its been a ball ache with having kept my own surname at times. I have been told by a bank that it was illegal to have kept my surname in the past! There's further complications if you married abroad too in terms of paperwork.
Certainly, if he's a British national but she isn't and there's a child involved and they've not got the paperwork in order with them for a marriage, again they'd be an requirement for a DNA test.
That may well also complicate eligibility for a UK passport for a child they have born abroad.
Further to that Iuliia appears to have possibly gone under the name Yuliya at some points in the UK.