According to a reliable contributor on one of the Practical Machinist Forums vices the fixed jaw on vices with that general style of bolt down mounting tend to lean back slightly at the top under clamping loads. Apparently even proper professional vices, such as Gerardi, can have a small, but still measurable when Inspector Meticulous is in full supercharge mode, deflection. So things may not be so bad under load. Pop something in it and use a lever indicator to see if things shift.
Obviously you have checked that the jaw plate is parallel and true.
What is the alignment of the moving jaw like?
If the moving jaw is true and the fixed jaw block seats well enough on the body consider applying smear of JB weld or similar metal loaded filler on the fixed jaw body before loosely inserting the jaw plates and lightly clamping the vice up squiggling excess filler out whilst bringing the jaws into mutual alignment. Grease or cling film on the jaw plates will do as a release agent. Its not quite that simple as some extra clamping will be needed to ensure the moving jaw doesn’t lift.
If they are both out a 1-2-3 block in the middle should work to do them both simultaneously.
There is a certain art to clamping when doing this sort of filler-in-place alignment as the moving reference parts need to be held tight enough not to lift yet be loose enough to slide. Stiffly.
Shimming is effective but can be a certain trial on patience. I never seem to have the right thickness in metal shims. The colour coded plastic shim sets are pretty good but they do have a mild tendency to squidge under serious loads. Which may be helpful for fine tuning.
The major issue with these inexpensive vices tends to be moving jaw lift. For conventional screw drive vices there is no substitute for accurate, close tolerance, manufacture if the vice is to work reliably and accurately. Pull down “acculock” devices can help but fundamentally these are the cherry on the top to make a well made vice work even better. On inexpensive products they invariably require fettling to work well and there are limits as to how much they can compensate for the less accurate fitting inevitable on a vice made to hit a low price point. As ever you get what you pay for and ordinary folk like us have to accept that when making £1 do the work of £5, or even £10, something must give.
I’ve long considered that treating a inexpensive vice as a casting kit to be converted to Chick pull down forwards or Gerardi push from the top of the back moving jaw operation might be a decent way of getting a better vice than you can directly afford. Basically slap a piece of gauge plate on top of the original base and have at it. The Chick pull rack looks do-able, an external screw to pull via a cross piece is far simpler than the internal arrangement o the real thing ought to work well enough. The pin through a hole locator for the push screw block on a Geraldi style is easier to make than the proper spring loaded ball in dimples albeit slower to use.
Clive