If you're serious about participating in public engagement, one way to improve your skills and connections can be to join networks of other communicators. In the UK, there are several well-established networks and you can benefit greatly from meeting others in the field, through sharing skills and training and connecting with opportunities.

• For maths communicators of all kinds, the UK network Talking Maths in Public runs a conference every two years, with smaller events and online sessions in between, as well as a chat group to keep in contact between events.
• For those who communicate research-level maths and statistics, the mathsci-comm Network aims to connect those working in, and with a stake in, communicating complex mathematics and data science to a variety of non-expert audiences in the UK. This includes researchers, media and communications professionals, those working in policy in government and non-government organisations.
• BIG is the UK STEM Communicators Network, and runs a mailing list, regular events and an annual conference (the BIG Event) in July. It's a great way to meet general science communicators in general, establish yourself as a contact and access their training and skills programmes. They run an annual Little Event for beginners in the field every January, and regular online socials during the pandemic.
• Various universities offer MSc courses/modules in Science Communication, which can be a great way to improve your knowledge and many can be completed as part-time study and/or remotely.
• Another way to get an insight into science communication events is to volunteer at science festivals - there are dozens around the UK and many take volunteers each year to help behind-the-scenes. It can be tough work, but they often cover expenses and you'll see a lot of how events are put together (and often get to meet some great people!)
• If you'd just like to meet others in the field on a casual basis, there's a network of Sci-comm Socials in the UK where you can join your local community, discuss science and maths communication and make contacts.