Welcome to the forum. Thanks for your question.
The symptoms of initial HIV infection are called the acute retroviral syndrome, or ARS. It always starts within a couple weeks of exposure and rarely lasts more than 4-6 weeks. Cold symptoms (runny nose, congestion, cough) are not part of the picture. And frequent colds also are not evidence of an than in those without it.
And a general point we have made repeatedly on this forum is that symptoms rarely are reliable indicators either for or against HIV. Even the most typical ARS or AIDS symptoms are nonspecific, i.e. they occur more commonly in other, usually minor medical conditions. If your case, it sounds like you and your partner have had allergies or just an unlucky series of colds.
So you are entirely correct that the answer to your anxiety about this is to be tested for HIV. While it seems your partner hasn't had sex with anyone else, multiple partnerships are very common amoung young gay men. Even in apparently monogamous relationships, all gay or bi men should have periodic routine testing for HIV (and other STDs), like once a year or thereabouts. On that basis alone, it's time for you to be tested -- but that advice has nothing to do with your symptoms.
So my advice is that both you and your partner visit your local NHS GUM clinic for routine HIV/STD testing (or a private sexual health clinic if you prefer and have the means, e.g. London's excellent Freedom Health Clinic). In the meantime, if your and your partner's sexual histories are accurate, you need not worry. You can expect negative test results.
Best wishes-- HHH, MD
Oh my gosh, I just nearly fainted after reading that "research suggests 1 in 7 men on the gay ‘scene’ in London is HIV positive". WHAT? I never imagined it was so widespread. I am absolutely terrified and sweating/shaking with worry right now.
I'm not sure about current estimates of the prevalence of HIV in London area men who have sex with men. One in 7 sounds too high for gay men in general, but it could be true for some, e.g. those who are frequently and outwardly unsafe (frequent anonymous partners, barebacking, etc). The GUM clinic will know; or you could look up information from the UK Health Protection Agency (HPA); I imagine they have a website and/or a public information phone number. The British Association for Sexual Health and HIV (BASHH) also would be an excellent source.