You can do this, but the risk of being refused entry will be less if you can secure an EEA family permit before you travel. (If your family member is a British national who lives in the UK, however, you generally will not qualify for one, because you will not be eligible to enter the UK under the EU freedom of movement regime.)
The UK has implemented the freedom of movement directive through The Immigration (European Economic Area) Regulations 2016. These regulations provide in part, at (11)(4), that
Before an immigration officer refuses admission to the United Kingdom to a person under this regulation because the person does not produce on arrival a document mentioned in paragraph (1) or (2), the immigration officer must ... allow the person to prove by other means that the person is ... (b) a family member of an EEA national with a right to accompany that EEA national or join that EEA national in the United Kingdom;
Accordingly, while you may or may not be issued an EEA family permit at the border, you should indeed be admitted if you have the following (this list is taken from the EEA family permit documents you must provide page):
- your passport
- your marriage certificate or other proof of your relationship
- if your wife is with you, her passport or identity card
- If your wife is not with you
- a copy of her passport or identity card
- evidence that she is in the UK and
- has been there for less than three months, or
- is a "qualified person" (working, studying, or self sufficient)
As your wife has been living in the UK since September 2016, you may be asked to show that she is a qualified person even if you are traveling with her, so it would be wise to bring evidence of her employment with you.
I recall reading on this site a story about a couple who were denied an EEA family permit, but admitted by an officer at juxtaposed border controls in France. I cannot find it now, perhaps because it was posted in the comments. As I recall, the person posting the story reported that the immigration officer expressed surprise or dismay at the refusal of the family permit and admitted the couple with no delay.