I am not entirely clear when you say "The newspaper is now almost 100 years old" whether you are referring to the title generally, which was first published in 1909, or the particular edition which you wish to re-publish. I'll assume it is the latter.
The problem is that a newspaper is a collective work (or as they are now known 'compilations') made up of a number of written pieces (literary works) and photographs (artistic works), each of which has a copyright term based on the lifetime of its author. So taking my assumption further, say the edition you want to re-publish came out in 1914, the applicable law at the time was the 1911 Copyright Act which said that the term of protection was the author's lifetime plus 50 years. But in order to know if the newspaper was now out of copyright, you would need to know the date of death of every contributor. Since some of them could quite reasonably be expected to be alive as recently as the 1980s or even the 1990s, clearly you cannot assume that a newspaper edition published in, hypothetically, 1914 is now out of copyright, especially since any author still alive in the summer of 1989 would automatically get the extra 20 years of post mortem protection introduced by the 1988 Copyright Designs and Patents Act.
Theoretically the authors (or more likely their heirs) of anything published in a newspaper between 1 July 1912 and 31 May 1957 have the right to veto the publication of their work outside of the newspaper even if they were employed journalists. However I think that is a technicality too horrendous to contemplate at this stage!
My advice would be, first, to seek permission from the Sketch's last owners, Associated Newspapers
, and only if that is unsuccessful, to approach the Newspaper Licensing Agency
as they will almost certainly expect you to pay for a (fairly expensive) licence.