You may quote a small portion of the article without the need for permission, using the quotation exception, along with the citation you mention. However, if you wished use the whole article or a major part of it, you would need to get permission. In 1960 Boothroyd was employed as an assistant editor on Punch and so as an employee copyright in the pieces he wrote for Punch would be owned by the magazine (see section 11(2) CDPA). However Punch is now defunct and it is not entirely clear to me exactly who now owns* the intellectual property. The cartoons appear to have been licensed to www.punch.co.uk who are trading as 'Punch Magazine'. However there is an entirely separate digital archive which appears to be owned or at least operated, by Gale. Unfortunately, their website contains no details about the intellectual property aspects. Nonetheless, I would try contacting Gale in the first instance about getting permission if you wish to quote the article in full.
* At the time the magazine first ceased publication in 1992 it was owned by United Newspapers (now UBM), and although Mohamed Al Fayed bought the title and briefly relaunched the magazine, I don't think he acquired the copyright in the original magazines. If you get nowhere with Gale, you could try contacting UBM to find out who they sold the intellectual property to, but I suspect that, as it was over 25 years ago, you may be met with a lot of blank looks (metaphorically speaking!).
It is, perhaps, worth noting that many Punch cartoons are now public domain in the UK, notwithstanding the fact that the aforementioned website is still offering to license them. The works of William Heath Robinson, for example, expired at the end of 2014, so anyone wishing to use them merely needs to source and scan an original copy of whichever issue of the magazine they appeared in, which may well be considerably cheaper than going through the website.