Firstly, who is the house builder as this will give a bearing on the likelihood of the issue being sorted out.
As you have LABC warranty (not a good sign - NHBC is better!) I believe it would probably e either Persimmon or Bloor Homes. At least you have not fallen into the trap of using the house builder's solicitor.
The warranty does not cover general snagging issues so the LABC or even NHBC would not cover this although they may help you in getting the house builder to act. The reality is, once a house builder has your money it can be extremely difficult to get them to remedy defects, let alone snagging.
This is why I always recommend that new home buyers get their home independently professionally snagged and inspected BEFORE legal completion and moving in. I would suggest you contact Martyn Maxwell at Brickkickers.co.uk. he will also be able to give you a written assessment of the colour variations in the mortar and brickwork.
These days with pre-mixed dry silo mortar, colour variations in mortar should be a thing of the past with the only variable being how much water is put in the mix and weathering. However, it may be a section of remedial work which hand mixed mortar was used for the making good. If the mortar colour varies a lot, and especially if it was site mixed (piles of sand bags of cement) it could be that the mortar is of varying strength and weak mortar would be serious and is a warranty issue.
The colour variation patches in your brickwork is a sign of a general lack of care and proper mixing of the bricks form different packs. This is quite common but this does not make it acceptable. As you say, you will see it every time you walk up to your home and it WILL bug you every time for years!
The cure for both mortar and bricks is a "Brick Doctor". The brick doctor will tint the bricks to blend in the colour variation and also tint the mortar too to achieve a consistent colour.
For the site manager it is just a phone call and a quick chat on site to explain what is required.
For the house builder it is a small bill of under £700.
If I were you, I would write to the housebuilder and say you are not going to legally complete until this matter has been resolved to your full satisfaction. Do not get bullied into doing otherwise!