I'm afraid it's a personal choice on which the final decision is up to you, and there are too many individual factors involved. Most of all how committed you are to moving to Canada. Or perhaps your health conditions first. Not all that much outsiders can tell you about moving.
As a bit of input, the vaccination rates in Canada have improved dramatically in the last 30-60 days, and on a quite fast pace. I expect that the mass vaccination phase will be what one could call something like complete by between end-July and end-August - at least to a level of say 60-70% of population vaccinated. New cases have fallen fairly dramatically too. So at least in one sense, it's hard to say that the UK is much safer (with respect to covid) than Canada (deaths are now low in both countries and new cases much lower in Canada - so at least the vaccine in UK is reducing severity but it's still there). Note, I'm not an expert on covid though, so personal opinion only. Perhaps consult your doctor.
So I guess you can watch how things proceed. If stable and trending down, apart from whatever additional issus with travelling itself, perhaps the risk balance is acceptable. At least perhaps by the end-summer timeframe you seem to be considering.
Note that while the Canadian government is advising against travelling generally, it has never banned outright and tried to limit to 'essential.' Moving to Canada is considered essential (at least for family sponsorship has been throughout). So while discouraging travel, and making it more difficult to reduce the amount of travel, the choice has been and is up to you. (Obviously if you expect that if you need to travel a lot after arriving, that's different risk than moving to Canada and remaining).
