There seems to be a clash between the increased secularization of the UK as well as the supposed islamification.
The former is definitely more apparent (and imo the latter is slightly exaggerated) and will seem to oppose any sort of rigorous Islamic influence imposed by Islamists.
Things like more halal food and stuff is just appealing to supply and demand. If a butcher lives in a heavily populated Muslim area, it would make sense for him to sell halal meat in order to make the most out of his business.
Because of the demographics, I'm afraid it is inevitable. The birth rate is much higher among Muslims. Obviously this will be in a generation's time but the percentage of Muslims will only increase.
Islam will have a greater say in the public and political arena in the UK. It is the second largest religion in the UK, and is the fastest growing religion in the UK. Thus, it is inevitable for the influence of Islam to grow further more as highlighted by the aforementioned documentary.
I hope to God it doesn't.