When you start cycling you have to get bike fit. Ride enough and that comes quickly and the muscles have built up- the ride position adapts and pesonal fitness comes in. takes about 3 to 6 months for most of us.

Next stage does not come in for a couple of years- and even then it is gradual. The big step came at the beginning.

Started riding 20 years ago and on some pretty aggressive offroad hills. I still have a marker hill for my performance and initially it took me 3 years to conquer it consistently. That came about by Getting bike fit initially- Getting personal fitness in and also getting the right bike for those hills. I still have that as a marker hill and I know I am doing OK if I can ride it. Know I am doing better if I do it in middle ring and the last stage of being really fit is when I do it just behind the fit bloke that is charging up the hill.

Interval training may help on Sprint speed but sounds like what you WANT is more overral speed. 15 to 16.5 MPH is not that bad but if you want to increase it- Then do as Hermes suggested- put more effort into the harder bits of the ride. Take the slight uphill section and stay in the same gear- keep the same cadence and push when it gets hard. I do that on a 400yard 4-5% slope we have on one of our rides. Start it at say 14mph and finish it at 14mph. By the end my legs are pumping up and the lungs are working.

Or up the milage to 40 to 60 and try to keep the same average

Or join the local club and go with the Group that are just above yout comfort zone.

All will work- but if I could manage 16.5 mph over a 40 miler on our hilly road rides- I would be ecstatic. Although saying that- My usual speed on a metric-100 kms or 65 miles- is 16mph. I think that is fast enough for me.