Crystal Palace is one of the UK's most powerful transmitters. You're 16 miles away. The Field dBuV gives a rough prediction of the kind of strength you should be able to pick up on the aerial without any amplification. 67dBuV is huge.
Unless your building is completely shadowed by surrounding buildings or trees, or your aerial is in a completely daft place such as pointing directly at the roof then there's very little justification to say that you need a higher gain aerial.
Further to that, the channel spread from the transmitter is all at the bottom end of the frequency spectrum. The UHF channel range runs from 21 to 60. Look at what Wolfbane shows you: 23, 26, 25, 30, 22, 28; all in the bottom half of the channel range. All in the place where high-gain wide band aerials work crap. Ergo, DO NOT buy a wide band high-gain aerial.
If you have a Log Periodic aerial but it is broken some how then replace it for another Log. That's the best choice for where you live. The aerial's response curve (which shows how effective it is at picking up TV transmissions vs frequency) means that it is the best choice for your area.
Make sure it is aligned properly. The boom should be fixed so that the little rods lay horizontal to the ground. This is what it means when Wolfbane says "Pol H"
Next, get it pointing in the right direction. That's the "Bearing Degrees" bit.
Replace the aerial downlead while you're doing the job. The cost is minimal. Don't waste your time and money saving a few pennies on cheap cable. If it doesn't have Webro WF100 written on the cable jacket then don't buy it. It's really that simple.
Fit the cable connectors properly... no half arsed job here please. No stray filaments touching the centre conduct. No spiders legs hanging out of the back of the F connectors.
As for the amplified splitter.... Unless the TV coax from the loft to the rooms is ancient "low loss" coax then with the amount of power your aerial is picking up you should have absolutely tonnes of signal to play with. A good passive splitter (i.e. not amplified) should be enough to feed all your TVs.
Put it another way, I live over 30 miles away from a TV transmitter that's only half as powerful as Crystal Palace. The aerial on my roof is also a Log Periodic. There's no amplification. Wolfbane says my Field Strength should be around 47dBuV, so that's quite a bit less than yours. I have enough signal to get 100% quality even after passive splitting it to two TVs.
Your problem might actually be too much signal.
Crazy as this might sound, once one has ruled out stupid mistakes like bad wiring, broken devices, crappy cable, nails through wires shorting out the conductor to earth etc etc then you start to look at the more exotic areas for answers. One is termination. Some amplified splitters work more effectively when the outputs are terminated. What that means in plain English is that an output socket left open with nothing connected to it can actually reduce the effectiveness of the amp. A TV is a 75 Ohm termination. By connecting a third TV you add another 75 Ohm termination on the amp. It stops the signals bouncing around. That might conceivably be enough to tip the signal level over the top of what the TVs need. So you might have too much signal rather than too little.
Look on this page
http://www.satcure.co.uk/accs/page15a.htm#variable for 'MA1620 Adjustable 0-20dB attenuator, coaxial connector version' You put these on the back of each TV. Turn it down so that you get the best signal QUALITY which is far more important than signal level.
If you're DIYing then a variable attenuator is just a great tool to have around for diagnostics.
If you still feel that the amplified splitter is a problem then cut your losses and replace it.
So, to recap, the correct type of aerial aligned properly, connected with some decent coax and correctly made connections and then a little attention to detail about signal quality. Job done.