Yes, Gatwick airport offers luggage offices in the North and South terminals for the convenience of passengers. It's a convenient place to store your baggage or belongings temporarily within operating hours 04.00 - 20:00. They will charge you for the time you store your luggage:
0-3 hours is £7.50 per item
After that, upon your first 24 hours, it is £12.50
From then onwards, 24-72 hours is £7.50 per 24 hours or part thereof, per item
After 72 hours, it is £5.00 per item, per 24 hours
You can also pre-book the luggage storage anytime online via left-baggage.co.uk/, or you can call them on 01293 569 900 to get assistance.