You say contract of employment so for this I assume they are employees and you are their employer.
The contract is therefore flawed, you can't override statutory entitlements by your own wording.
You can't say you won't pay them holiday - that will be in breach of the working time directive.
You can't say you won't pay them as they will at least be entitled to statutory notice period.
I can't see how you can enforce the clause about them having to tell you if other employment is secured - how are you going to manage that, and what business is it of yours if they do find another job.
Less than two years and working part time is irrelevant really as far as the procedure goes though for redundancy the 2 years is relevant for pay.
An employee can bring a claim to employment tribunal for unfair dismissal after 1 years service.
For the process, write a letter saying job is at risk and invite them in, then explain the situation and business grounds. Techinically you should then have some meaningful consultation - suggest a week or so to look at alternative options and if the job is definitely redundant, dismiss them in a meeting (write to them and tell them what it is about again) and give right of appeal. If they appeal (can't see that they would have grounds), someone else in the business to hear it and write with the outcome.
This is all about best practice and protecting the company from claims.
Suggest you learn some basic employment law if you are running a business and get some legal advice about writing contracts of employment!