Canadian Student Wanting to Finish my Thesis in UK to be with my Partner

I am a Canadian graduate student studying Engineering in Canada. My partner is a British graduate student studying English Literature in Wales. We lived together in Canada for 6 months before they left. I want to live in Wales, starting in February, to be with my partner while I finish writing my thesis and then return to Canada in April or May to give my defence and finish my degree. My partner is living in university residence and according to her lease, I can not live with her. I have $50000 in savings and plan to rent an apartment close by while I am there. I don’t plan to be employed while I am there but I will need to bring some lab equipment with me to support the writing of my thesis. Because I will be there for less than 6 months, I think I do not need a Visa but I’m worried about being questioned about my equipment when I go through Customs. Will this be a problem? Should I bring a letter from my supervisor that explains my situation?

Also, after finishing my degree I hope to find work as an Engineer in the UK but I don’t know how long it will take to find a job. If I stay in Wales for 4 months, return to Canada for a month, and then go back to Wales, how long can I stay in Wales before I will need a Visa?