I'd never heard of InvestEngine (IE) so went and had a look at their website. One of the problems, which I think you'll have found, is that it's difficult to make a direct comparison on fees because they do not, by any stretch of the imagination, offer identical products; and IE is somewhat less than honest in the assumptions it makes when comparing fees; for example, they appear to be using AJ Bell's ISA charges instead of its SIPP charges in the comparison table.
AJ Bell's SIPP has a monthly share-holding account charge of 0.25% which maxes out at £10 per month (not £3.50 per month, which is what IE says on the comparison table), a separate fund-holding charge of up to 0.25%, and a £5 trading fee. However, trading fees on AJ Bell drop to £3.50 per trade if you trade more than 10 times in the previous month (which IE acknowledge) and they are only £1.50 per trade if it's set up as a regular investment (which IE does not acknowledge).
IE offer a SIPP with no account charges on the DIY version, and no trading fees.
The problem with IE is that to offer such low fees, they bundle up all their customers' trades together in one daily transaction, and they only let you trade in ETFs (exchange traded funds). You cannot, for example, buy individual company shares, gilts, bonds, or funds in your IE SIPP.
IE don't state what spread they operate - this is the difference between selling and buying prices and while there is always a small spread because of the way markets work, they can make money out of you by operating a much wider one and pocketing the difference, particularly if they are concentrating everyone's activity into one daily transaction. It's a bit like how £2000 buys you a much better exchange rate from the Post Office than £100 does from the Travelex kiosk at the airport, and how both of then screw you when you sell your surplus euros back.
IE also make money by using your uninvested cash for themselves. AJ Bell pay interest.
If you want to use IE's 'managed' portfolios - where you choose a level of risk and they keep everything balanced to that risk tolerance - then you pay fees (0.25% pa) for that too. If you opt for AJ Bell's similar 'ready made pension' then they charge 0.45%.
If you wanted your entire SIPP in ETFs only, and a bunch of computers doing things with your money in the background to keep costs down, then I guess IE might work for you.
My SIPP is with AJ Bell and their fees don't frighten me because they are actually good value from a proper full service stockbroker. I can buy almost any traded asset in the world which is eligible for holding in a SIPP, they offer competitive prices, and the trade is more or less instantaneous. They also have a team of investment experts who share their insight and market commentary with investors, and they have actual living, breathing customer services representatives on the end of the phone when things go wrong.