I'm in the same boat - single and longing for a child - so I really wish you didn't have to hear this, but you have left it too late to have your eggs frozen.
I found, when doing my research, that the cut-off age is 35, and in many clinics it's 32. They can and do make exceptions (for people with cancer, for example), but as someone has posted above, the success rate from these eggs is exceptionally poor and many reputable clinics don't offer the freezing of unfertilised eggs at all for this reason.
If you can access donated sperm (from a sperm bank, or a known donor), you could have IVF, and then have any resulting embryos frozen, although normally you'd be expected to have at least one embryo transferred immediately. The success rate of IVF is also poor, and it's expensive. The majority of women aged 35+ need 3 cycles and that can easily cost £30k. If you can afford this, get treatment immediately. Most NHS trusts will offer one free cycle of IVF, but the cut-off is 42 and the waiting list is long.
Having said that, if you have established you're both physically and hormonally fertile (so had all the blood tests and a dye scan), you may find you're fertile for a lot longer than the medical statistics would suggest. I know many women who have had natural pregnancies right up until the age of 45. One day I hope to join their number, and I hope you will too.