Is it Legal to Ride a Penny-Farthing on Public Roads?

In a word, the answer is “yes“, but in accordance with the Highway Code like any other road user. 

The Highway Code is not just legal technicality: it defines proscribed, standardized ways of vehicle operation that make our actions predictable to other road users who are than able to anticipate our actions to avoid collisions.

Don’t be selective in abiding by the Highway Code. Once you deviate from the Highway Code and start doing random things, you create confusion and set the stage for an accident. And if you confuse motorists, you the Penny-Farthing rider will be the one that suffers the consequences. 

If you’re a bit rusty on your Highway Code, swot-up on it in respect to your responsibilities as a cyclist and motorists’ responsibilities to you as a cyclist before venturing out onto the UK’s busy, dangerous roads on your Penny-Farthing:

https://www.gov.uk/guidance/the-highway-code/introduction

To learn about how the Highway Code specifically relates to Penny-Farthings, I wrote this definitive guide which has been subjected to extensive peer review, so the content should be correct:

https://bicycles.stackexchange.com/a/73454/52565