Burnett's gin is pretty traditional and light. It's not a great brand, not bottom shelf but near it. Go with any traditional London Dry gin. Bombay, Tanqueray, Beefeater, Gordons. Bombay Sapphire is not similar at all and wouldn't be what I would recommend. It's popular but I don't care for it when there are dozens of great gins out there. Where are you located?
If you go through this link you can read some of my gin reviews, if you go back far enough you can read at least fifty of them. I have Burnett's in my to do pile and will get around to it when I make it past some of the better ones.