Looking for accommodation in the UK can be a time-consuming and nerve-wracking experience. Whatever you do, give yourself plenty of time as you will be much more likely to get what you are looking for this way.
It's best to start looking before you leave or plan for free time to be dedicated to the search. If you are coming with your family, it may be more comfortable for them to arrive after you have found suitable accommodation. If you are arriving alone, the best solution may be to initially stay in a hotel/guest-house or with friends or acquaintances.
Unless you want to depend on getting lucky, you should consider several options for your apartment search. The most important thing is to have a very clear idea of what you're actually looking for, or it is very easy to waste time. The best start is to get familiar with your new environment by walking around, seeing how transport works and asking other people about different neighbourhoods and areas.
On arrival in the UK, you may find it necessary to stay in temporary accommodation for a few weeks or a month or two until you can move into an apartment. Many hotels and bed-and-breakfast establishments cater for long-term guests and offer reduced weekly or monthly rates.
There is a wide range of options when looking for an apartment. As always in life, the more you're willing to pay (i.e. for an agent), the easier your search will be.