In the United Kingdom, the Copyright Designs & Patents Act 1988 specifically allows the use of fonts without infringing copyright.
54 Use of typeface in ordinary course of printing.
(1) It is not an infringement of copyright in an artistic work consisting of the design of a typeface—
(a) to use the typeface in the ordinary course of typing, composing text, typesetting or printing,
(b) to possess an article for the purpose of such use, or
(c) to do anything in relation to material produced by such use;
and this is so notwithstanding that an article is used which is an infringing copy of the work.
However you do commit an offence if you don't get the correct licence for the font in the first place. You need the right licence to create the copies of the fonts you intend to use: perhaps a straightforward TTF file, maybe a web-font version or something else.
17 Infringement of copyright by copying.
(1) The copying of the work is an act restricted by the copyright in every description of copyright work; and references in this Part to copying and copies shall be construed as follows.
(2) Copying in relation to a literary, dramatic, musical or artistic work means reproducing the work in any material form.
This includes storing the work in any medium by electronic means.
You may find that the font owner will only charge a low fee to allow you to download the font and produce the versions you need to use. Once you have the font, the font owner can't impose royalty charges in the UK.
Other jurisdictions may differ.
This answer does not provide definitive legal advice in the UK or other jurisdictions. If you want legal advice, ask a lawyer.