In the UK the answer is you can, but the chances of them flowering are very slim.
Sunflowers take around 2 and a half to 3 months from sowing to flowering. So from planting the seeds in august would mean they should flower around November and December.
The chances are that the plants will die off before they flower due to the cold weather, and even if they do flower the display will be very short-lived.
If you are growing them indoors in a greenhouse or polytunnel then you stand a much higher chance of being successful. The temperatures in your greenhouse will be a lot milder than they will outdoors which will give the sunflowers a chance at surviving long enough to bloom.
whether you are successful or not will depend a lot on the weather that year, if we have a miserable wet summer then you stand less of a chance.
If we have a really warm and sunny summer (but not a drought!) then you will have a much better chance. How soon the first frosts arrive will also affect how successful you are.
If you provide the plant with everything it needs and we have really good autumn then maybe you will see flowers but the chances are small. The further south you are the better chance you have of being successful here and if you are in Cornwall then you stand an even greater chance due to the unique micro-climate there.
Sowing Sunflowers In August
Sunflowers don’t like root disturbance so direct sowing is preferred. This is one advantage of summer sowing as the soil will be nice and warm and perfect for germinating sunflower seeds.
Once they have got going feed them regularly, this is advised will all sunflowers as they are hungry plants but it is imperative with late sowings.
The more you feed the quicker they will grow (up to a limit, overfeeding can be a problem!) so weekly feeds can help your August-sown sunflowers to make up for the lost time.