Do I understand that actually you are only intending this for 3 years - R.,1 and 2 (because this is what you can afford)?
I would only consider doing this if your local state schools are separate infant and junior schools. IME as a parent and as a teacher, children who join schools at a 'natural' transition point (start of primary, start of juniors if separate school, start of secondary, start of 6th form) have a MUCH easier time a) accessing the school and b) settling in than those who transition at other times.
Do not underestimate the difficulty of re-entering the state primary system at year 3, just from the admissions point of view, btw. Although Infant Class Size Regulations only apply up to the end of Y2 - so a Y3 class can have >30 children in a class - most schools still have PANs of 30 and so getting in for Y3 will require an appeal. Popular schools may already be highly over-subscribed, and 'I ran out of money to pay the private school fees' isn't a good reason to admit on appeal, so you are likely to be offered a place in a less good, under-subscribed school further away rather than one in a good local school that you might have got into at reception.
As to whether those years at primary are worth it, it depends critically on the schools in question. As a state school, we admit a fair number of children who leave local private schools, and in every case in my memory those have been children who have been behind, of ten dramatically behind, their peers in the state sector - but that is primarily because the private schools locally manage out children who will not look good in their exit statistics at the end of Y6.
In your position I would ONLY go for it if
a) The schools locally are separate infant and junior schools, so transferring at Y3 to a new school is 'normal'
b) You are absolutely confident of getting a place in your preferred sate school at the start of Y3
or
c) You can actually manage it until the end of Y6, and the state secondary has a reasonable number of privately educated children enter every year. Like others, I live in an area where private primaries coaching children intensively for the 11+ is a serious industry, and so the local selective schools have decent sized privately-educated intakes (10-25%) . In contrast, the non-selective secondaries have vanishingly tiny intakes from private primaries.