No. Every worker has a right, by law, to choose whether or not to belong to a trade union. Action by the employer aimed at preventing a worker from exercising this right, whether at the recruitment stage, during employment or by termination of employment, is unlawful.
If your employer tries to prevent or discourage you from joining a union, for example by threatening you with the loss of a benefit, or by offering you some benefit in return for not joining, seek advice as early as possible. The union will be well placed to sort things out.
Under section 145A of the Trade Union and Labour Relations Consolidation Act 1992, it is unlawful for an employer to offer a worker an inducement not to join a union or not to take part in union activities.
It is also against the law for your employer to refuse you employment, dismiss you or subject you to any detriment because your name appears on a ‘blacklist’ (a list of individuals who have been or are trade union members, or who have taken or are taking part in trade union activities). The relevant law is regulation 5 of the Employment Relations Act 1999 Blacklists Regulations 2010.