The compressive effect on the body itself is not a problem because we are composed of incompressible fluids and solids. All gas filled cavities in a healthy person are connected by tubes to the outside so that the internal pressure can be equalized as external pressure increases.
A deep diver is affected by a variety of other problems that can be corrected by adjusted the gas mixture.
Nitrogen is a narcotic that affects judgement as depth increases. This can become significant from 30m and is seriously dangerous from 50m down. The effect is mitigated a little by getting used to deep diving, but the sensible way to avoid nitrogen narcosis is to use a breathing mixture with less nitrogen. All gas toxicity problems are dependent on partial pressure so if you replace half the nitrogen with helium which is not toxic you can go to twice the depth without narcosis.
Oxygen is toxic with very different symptoms. It normally causes spasms and fits at 80m with probably fatal consequences. Again the remedy is to replace oxygen with helium but you need to keep enough oxygen to breath.
Despite these toxicity problems some people claim to have reached depths up to 155m on air for brief moments. It is almost suicidal to attempt anything deeper than 100m on air.
To go deeper you can use a mixture of helium and oxygen but at about 250m you start to suffer from High-pressure nervous syndrome. This is not a gas toxicity problem but a direct effect of pressure on the functioning of the nerves causing shaking. Luckily this can be corrected by adding just the right amount of nitrogen back into the gas mix. It is as if narcosis and HPNS have opposite effects that cancel each other out.
Using the right mixture of oxygen, nitrogen and helium it has been possible to go deeper. The record is unofficially 318m by Nuno Gomes in 2005. Problems are to control the gas mixture ratios as you go deeper. Off course it can take weeks to decompress allowing the gas dissolved in blood and tissue to escape slowly without blocking blood vessels or nerves. You also need to control the temperature of the gas carefully because helium at high density has a high heat capacity and hypothermia is a potential problem. The viscosity of the gas mixture also makes breathing more difficult as pressure increases.
It is likely that there are other unknown problems that would limit diving long before reaching 700m without hard suits.
Deepest escape from a submarine without scuba is probably about 65m, two survivors from HMS P32 1941. The short exposure to pressure in such circumstances means that decompression is not a serious problem but they need to breath out constantly on the way up as the gas in their lungs expands.