There is no point in being too exact in these figures as they could vary hugely depending on how it was done.
BookstockThe total capacity of Kilburn library is about 32,000 so 140,000 volumes is a lot. Assuming that the stock if bought at say £8 or £9 per volume (the cheaper end of the pricing I would have thought), and you are looking at a bookstock fund of about £1.2 million. If the institution wanted more specialist items (e.g. foreign languages, large textbooks, a lot of audio books) I would imagine the prices would be higher. £1.2 million would be about three times Brent's annual bookstock fund.
Where is that money going to come from?
There is no direct mention of most of the information technology which many people now consider essential to a library, or other services such as Wifi, e-lending, periodicals and so on. There is also no mention of things that have triggered challenges in other places such as provision of training, facilities management and so on.
To make this building available in a way remotely comparable to a Brent Library would incur all sorts of costs that appear not to be budgeted for.