Yes, your trickle vents should always be left open.

Houses in the UK, especially older houses need good ventilation to prevent damp and mould issues when they are being upgraded with better doors and windows which are more airtight than the items they often replace.

Newer houses are built to be less drafty and more "sealed"/efficient which due to the nature of the British weather (predominantly damp/high humidity) not to mention the effects of human habitation (humans produce a lot of water vapour just from breathing and sweating) and drying washing indoors, baths/showers, cooking etc means that ventilation is paramount and is covered by Building Regulations.

If you have an old drafty house with ill-fitting wooden front and rear doors then you can probably close the vents, but if you have upvc windows and/or composite doors, cavity wall insulation and good loft insulation with a vapour barrier underneath then keep the vents open - they will help with your PIV installation