Group insurance is based on the WHOLE group experience and census, not on just you. Individual insurance is based on just you. So naturally the rates are going to be different. OF COURSE it's legal for your employer to increase your rate and OF COURSE it's legal for you to purchase other coverage.
However, there are a few things you need to remember. Under IRS regulations, if your employer group plan is subject to Section 125 regulations (and it almost certainly is) you can ONLY drop coverage during open enrollment, or when you have a qualifying event. If this is your open enrollment period, no problem, you can drop coverage through your employer with no questions asked. But if it's not your OE period, you will need to provide written verification from the other insurer that you have already obtained other coverage and the date on which it started. Without that (and without whatever other forms your employer may require for a mid-year change), your employer not only need not, but must not, allow you to drop coverage.
Usually you only have 30 days to make this change, so you don't want to waste time. Call your HR office and confirm whether it is OE and if not, what documentation they require to do a mid-year change.