That's because the smallest (Smaller means more revolutions to one crank from the front, ie. 52/14 = 3.7 turns of the rear wheels.)  The 7 speed starts from 14 cogs to 28 cogs maximum. The normal smallest cogs for an 8,9 and 10 speed are 11 cogs. So that's 3 steps higher gear higher than your D7. The cheapest way that I can see here is like this ;

Presume that it is an 11T at the rear, that means 52/11 = 4.7 turns. Take this as a bench level. Let's say now, we change the front chain ring to 58 teeths. This is 58/14 = 4.14 turns. That is still lower than the bench mark! In this case, for your D7, you need to change the whole crank/chainring as they are one piece! This option is expensive and still doesn't reach your objective.

OK, another solution. I saw a freewheel cog (the type that 7 speeders use ) the other day, in Joo Ngan Son, an 8 speed one that starts from 11T to 30T.  For this you just change the freewheel hub ( presuming it is still there, else you need to order ) and also another 8 speed shifter. The existing RD should be able to handle another step up. Here , your high gear goes up 3 notches and lower gear another notch.

Alternatively, change the wheelset for about 400 bucks. Get a better wheelset with sealed bearings and use the common cassette with the free wheel on the hub. For this, I am sure you will go for the max 10 speed or at least 9 speed, I mean mean why stick to 8 speed , right?   Here you need to change the RD and the shifter in addition to the wheelset.

If you are already riding the way you describe, I would rather go for the third option, though expensive, it's the ultimate need. Sealed bearing hubs makes a lot of difference in ride performance, so it is worthwhile. First option you have to spend quite a lot too as a cheap crank will set you 150 bucks but the 58 teeth or 60 teeth chainring will be expensive. So, not worthwhile! If you don't want to spend on wheelset, then option 2 suits you.

I saw an 8 speed freewheel sold in BBS but it still starts from 13T and this does not fit your criteria. Usually riders have problems on the lower gears but yours is on the higher gears. 
http://bicyclebuysell.com/item/300708/sunr...el-free-pos-w-m

That's because the smallest (Smaller means more revolutions to one crank from the front, ie. 52/14 = 3.7 turns of the rear wheels.)  The 7 speed starts from 14 cogs to 28 cogs maximum. The normal smallest cogs for an 8,9 and 10 speed are 11 cogs. So that's 3 steps higher gear higher than your D7. The cheapest way that I can see here is like this ;

Presume that it is an 11T at the rear, that means 52/11 = 4.7 turns. Take this as a bench level. Let's say now, we change the front chain ring to 58 teeths. This is 58/14 = 4.14 turns. That is still lower than the bench mark! In this case, for your D7, you need to change the whole crank/chainring as they are one piece! This option is expensive and still doesn't reach your objective.

OK, another solution. I saw a freewheel cog (the type that 7 speeders use ) the other day, in Joo Ngan Son, an 8 speed one that starts from 11T to 30T.  For this you just change the freewheel hub ( presuming it is still there, else you need to order ) and also another 8 speed shifter. The existing RD should be able to handle another step up. Here , your high gear goes up 3 notches and lower gear another notch.

Alternatively, change the wheelset for about 400 bucks. Get a better wheelset with sealed bearings and use the common cassette with the free wheel on the hub. For this, I am sure you will go for the max 10 speed or at least 9 speed, I mean mean why stick to 8 speed , right?   Here you need to change the RD and the shifter in addition to the wheelset.

If you are already riding the way you describe, I would rather go for the third option, though expensive, it's the ultimate need. Sealed bearing hubs makes a lot of difference in ride performance, so it is worthwhile. First option you have to spend quite a lot too as a cheap crank will set you 150 bucks but the 58 teeth or 60 teeth chainring will be expensive. So, not worthwhile! If you don't want to spend on wheelset, then option 2 suits you.

I saw an 8 speed freewheel sold in BBS but it still starts from 13T and this does not fit your criteria. Usually riders have problems on the lower gears but yours is on the higher gears. 
http://bicyclebuysell.com/item/300708/sunr...el-free-pos-w-m

there are plenty of freewheel 7 speed, 11-28/30 even megarange 34t over in taobao.

u can change the crankset too to get more teeth,... 
if u know what to look for...
won't cost u alot....